Measuring electrical parameters of power line operation, using a digital computer

• US 5,301,121 A
• Filed: 07/11/1991
• Issued: 04/05/1994
• Est. Priority Date: 07/11/1991
• Status: Expired due to Fees

• Current Assignee: General Electric Company
• Original Assignee: General Electric Company, Yokogawa Electric Corporation
• Inventors: Nishijo, Masaaki, Imamoto, Masami, Fujino, Kenji, Garverick, Steven L.
• Primary Examiner(s): Harvey, Jack B.
• Assistant Examiner(s): CHOI, KYLE JAEHUN
• Application Number:
  US07/728,408
• Time in Patent Office: 999 Days
• Field of Search: 364/572, 364/483, 364/481, 364/492, 364/571.01, 364/571.08, 324/115
• US Class Current: 702/60
• CPC Class Codes: G01R 19/25 using digital measurement techniques
• CPC Class Codes: G01R 21/1331 Measuring real or reactive component, measuring apparent energy
• CPC Class Codes: G01R 35/04 of instruments for measuring time integral of power or current

Abstract

A method for measuring at least one electrical parameter of the operation of a p-phase power line, p being a positive integer, arranges respective sensing apparatus to sense at least one of the voltages and currents associated with each phase of the power line. Analog-to-digital conversion apparatus is used to digitize the response of each sensing apparatus, thereby to generate corresponding digital responses. A digital computer is used to correct each digitized response of the analog-to-digital conversion apparatus for non-linearities, gain errors and phasing errors in the responses of the sensing apparatus and for non-linearities and gain errors in the responses of the analog-to-digital conversion apparatus. The computer is used to high-pass digitally filter each digital response that has been corrected, in order to suppress any attendant direct term. The digital computer then calculates each the electrical parameter, proceeding from each digital response that has been corrected and has been high-pass digitally filtered.

Claims

1. A method for measuring at least one electrical parameter of the operation of a p-phase alternating-current power line, p being a positive integer, said method comprising the steps of:

arranging respective sensing apparatus to sense at least one of the voltages and currents associated with each phase of said power line;

using analog-to-digital conversion apparatus to digitize the response of each sensing apparatus, thereby to generate a corresponding digital response;

using a digital computer to correct each digitized response of said analog-to-digital conversion apparatus for non-linearities and gain errors in the responses of said sensing apparatus and said analog-to-digital conversion apparatus;

using the digital computer to high-pass digitally filter each digital response that has been corrected for non-linearities and gain errors, in order to suppress any attendant direct term; and

using the digital computer to calculate each said electrical parameter, proceeding from each digital response that has been corrected for non-linearities and gain errors and has been high-pass digitally filtered.

2. The method of claim 1 including the additional step of:

supplying a calculated electrical parameter from said digital computer to apparatus generating indications of the calculated electrical parameter of a form perceptible to a human being.

3. The method of claim 2 wherein the additional step of supplying a calculated electrical parameter from said digital computer to apparatus generating indications of the calculated electrical parameter of a form perceptible to a human being comprises applying the calculated electrical parameter to a digital read-out device.

4. The method of claim 2 wherein the additional step of supplying a calculated electrical parameter from said digital computer to apparatus generating indications of the calculated electrical parameter of a form perceptible to a human being comprises the substeps of:

using a pulse-duration modulator to generate pulses having a duration directly related to the calculated electrical parameter from said digital computer; and

applying the pulses to a D'"'"'Arsonval meter.

5. The method of claim 1, employed for measuring the r-m-s value of a voltage associated with a power line phase of a p-phase alternating-current power line having p+1 conductors including a neutral conductor and at least one other conductor, wherein said step of arranging respective sensing apparatus to sense at least one of the voltages and currents associated with each phase of said power line includes arranging a voltage sensing apparatus to sense the voltage associated with the phase of said power line the r-m-s voltage of which is being measured, as referred to a voltage appearing on said neutral conductor, thereby to generate an analog signal for being digitized using said analog-to-digital conversion apparatus, and wherein said step of using the digital computer to calculate each said electrical parameter comprises the substeps of:

squaring the digitized response to signal from said voltage sensing apparatus after it has been corrected for non-linearities and gain errors and has been high-pass digitally filtered,

low-pass digitally filtering the squared digitized response to generate a low-pass filter response, and

taking the positive square root of said low-pass filter response to calculate the r-m-s voltage associated with the power line phase.

6. The method of claim 1, employed for measuring the r-m-s value of a voltage associated with a power line phase of a p-phase alternating-current power line having a respective conductor for each phase, p being at least three, wherein said step of arranging respective sensing apparatus to sense at least one of the voltages and currents associated with each phase of said power line includes arranging a voltage sensing apparatus to sense the voltage associated with the phase of said power line the r-m-s voltage of which is being measured, as referred to the voltage associated with another phase of said power line, thereby to generate an analog signal for being digitized using said analog-to-digital conversion apparatus, and wherein said step of using the digital computer to calculate each said electrical parameter comprises the substeps of:

squaring the digitized response to signal from said voltage sensing apparatus after it has been corrected for non-linearities and gain errors and has been high-pass digitally filtered,

low-pass digitally filtering the squared digitized response to generate a low-pass filter response, and

taking the positive square root of said low-pass filter response to calculate the r-m-s voltage associated with the power line phase.

7. The method of claim 1, employed for measuring the r-m-s value of a current associated with a power line phase, wherein said step of arranging respective sensing apparatus to sense at least one of the voltages and currents associated with each phase of said power line includes arranging a current sensing apparatus to sense the current flowing through a power line conductor associated with the phase of said power line the r-m-s current of which is being measured, thereby to generate an analog signal for being digitized using said analog-to-digital conversion apparatus, and wherein said step of using the digital computer to calculate each said electrical parameter comprises the substeps of:

squaring the digitized response to signal from said current sensing apparatus after it has been corrected for non-linearities and gain errors and has been high-pass digitally filtered,

low-pass digitally filtering the squared digitized response to generate a low-pass filter response, and

taking the positive square root of said low-pass filter response to calculate the r-m-s current associated with the power line phase.

8. The method of claim 1, employed for measuring the r-m-s value of a voltage associated with a power line phase of a p-phase alternating-current power line having p+1 conductors including a neutral conductor and at least one other conductor, wherein said step of arranging respective sensing apparatus to sense at least one of the voltages and currents associated with each phase of said power line includes arranging a voltage sensing apparatus to sense the voltage associated with the phase of said power line the r-m-s voltage of which is being measured, as referred to a voltage appearing on said neutral conductor, thereby to generate an analog signal for being digitized using said analog-to-digital conversion apparatus, and wherein said step of using the digital computer to calculate each said electrical parameter comprises the substeps of:

calculating the frequency of the digitized response to signal from said voltage sensing apparatus after it has been corrected for non-linearities and gain errors and has been high-pass digitally filtered;

squaring the digitized response to signal from said voltage sensing apparatus after it has been corrected for non-linearities and gain errors and has been high-pass digitally filtered;

low-pass digitally filtering the squared digitized response to generate a low-pass filter response,

generating the kernel for said substep of low-pass digitally filtering with a width determined from the calculated frequency of the digitized response to signal from said voltage to extend over an integral number of cycles of said voltage associated with a power line phase; and

taking the positive square root of said low-pass filter response to calculate the value of the r-m-s voltage associated with the power line phase.

9. The method of claim 1, employed for measuring the r-m-s value of a voltage associated with a power line phase of a p-phase alternating-current power line having a respective conductor for each phase, p being at least three, wherein said step of arranging respective sensing apparatus to sense at least one of the voltages and currents associated with each phase of said power line includes arranging a voltage sensing apparatus to sense the voltage associated with the phase of said power line the r-m-s voltage of which is being measured, as referred to the voltage associated with another phase of said power line, thereby to generate an analog signal for being digitized using said analog-to-digital conversion apparatus, and wherein said step of using the digital computer to calculate each said electrical parameter comprises the substeps of:

calculating the frequency of the digitized response to signal from said voltage sensing apparatus after it has been corrected for non-linearities and gain errors and has been high-pass digitally filtered;

squaring the digitized response to signal from said voltage sensing apparatus after it has been corrected for non-linearities and gain errors and has been high-pass digitally filtered;

low-pass digitally filtering the squared digitized response to generate a low-pass filter response,

generating the kernel for said substep of low-pass digitally filtering with a width determined from the calculated frequency of the digitized response to signal from said voltage to extend over an integral number of cycles of said voltage associated with a power line phase; and

taking the positive square root of said low-pass filter response to calculate the value of the r-m-s voltage associated with the power line phase.

10. The method of claim 1, employed for measuring the r-m-s value of a current associated with a power line phase, wherein said step of arranging respective sensing apparatus to sense at least one of the voltages and currents associated with each phase of said power line includes arranging a current sensing apparatus to sense the current flowing through a power line conductor associated with the phase of said power line the r-m-s current of which is being measured, thereby to generate an analog signal for being digitized using said analog-to-digital conversion apparatus, and wherein said step of using the digital computer to calculate each said electrical parameter comprises the substeps of:

calculating the frequency of the digitized response to signal from said current sensing apparatus after it has been corrected for non-linearities and gain errors and has been high-pass digitally filtered;

squaring the digitized response to signal from said current sensing apparatus after it has been corrected for non-linearities and gain errors and has been high-pass digitally filtered,

low-pass digitally filtering the squared digitized response to generate a low-pass filter response,

generating the kernel for said substep of low-pass digitally filtering with a width determined from the calculated frequency of the digitized response to signal from said current to extend over an integral number of cycles of said current associated with a power line phase; and

taking the positive square root of said low-pass filter response to calculate the value of the r-m-s current associated with the power line phase.

11. A method for measuring at least one electrical parameter of the operation of a p-phase power line, p being a positive integer, said method comprising the steps of:

arranging respective current sensing apparatus to sense the analog current flow in each phase of said power line;

arranging respective voltage sensing apparatus to sense the analog voltage across each phase of said power line;

using analog-to-digital conversion apparatus to digitize the response of each current sensing apparatus and of each voltage sensing apparatus, thereby to generate corresponding digital responses;

using a digital computer to correct the digitized responses of said analog-to-digital conversion apparatus for non-linearities and gain errors in the responses of said current sensing apparatus and said voltage sensing apparatus and said analog-to-digital conversion apparatus;

using the digital computer to high-pass digitally filter the digital responses that have been corrected for non-linearities and gain errors, in order to suppress attendant direct terms;

using the digital computer to calculate the frequency of one of the digital responses that has been corrected for non-linearities and gain errors and has been high-pass digitally filtered;

using the digital computer to response to the calculated frequency to generate a phase correction of the digital response to each current sensing apparatus that has been corrected for non-linearities and gain errors and has been high-pass digitally filtered; and

using the digital computer to calculate each said electrical parameter, proceeding from the digital responses that have been corrected for non-linearities and gain errors, have been high-pass digitally filtered, and have been phase-corrected.

12. The method of claim 11 wherein said step of using the digital computer to calculate each said electrical parameter includes substeps of:

low-pass digitally filtering to generate a low-pass filter response, and

generating the kernel for said substep of low-pass digitally filtering with a width determined from said calculated frequency to extend over an integral number of cycles of said electrical parameter.

13. The method of claim 12, employed for measuring the real power of a single power line phase, wherein said step of using the digital computer to calculate each said electrical parameter comprises the substeps of:

multiplying the digitized response to signal from said voltage sensing apparatus for said single power line phase, after it has been corrected for non-linearities and gain errors and has been high-pass digitally filtered, by the digitized response to signal from said current sensing apparatus for said single power line phase, after it has been corrected for non-linearities and gain errors, has been high-pass digitally filtered and has been phase-corrected, thereby to generate a digital product signal; and

low-pass digitally filtering the digital product signal to generate a low-pass filter response that corresponds to a calculation of the real power for said single power line phase.

14. The method of claim 12, employed for measuring the real power of a plural-phase power line, wherein said step of using the digital computer to calculate each said electrical parameter comprises the substeps of:

for each phase, multiplying the digitized response to signal from said voltage sensing apparatus for that phase, after it has been corrected for non-linearities and gain errors and has been high-pass digitally filtered, by the digitized response to signal from said current sensing apparatus for that phase, after it has been corrected for non-linearities and gain errors, has been high-pass digitally filtered and has been phase-corrected, thereby to generate a respective digital product signal for that phase;

adding together the respective digital product signals for all the phases to generate a digital sum signal; and

low-pass digitally filtering the digital sum signal to generate a low-pass filter response that corresponds to a calculation of the real power of the plural-phase power line.

15. The method of claim 12, employed for measuring the reactive power of a single power line phase, wherein said step of using the digital computer to calculate each said electrical parameter comprises the substeps of:

phase-shifting by ninety degrees the digitized response to signal from said voltage sensing apparatus for said single power line phase, after it has been corrected for non-linearities and gain errors and has been high-pass digitally filtered, thereby to generate a digital quadrature voltage response;

multiplying the digital quadrature voltage response by the digitized response to signal from said current sensing apparatus for said single power line phase, after it has been corrected for non-linearities and gain errors, has been high-pass digitally filtered and has been phase-corrected, thereby to generate a digital product signal; and

low-pass digitally filtering the digital product signal to generate a low-pass filter response that corresponds to a calculation of the reactive power for said single power line phase.

16. The method of claim 12, employed for measuring the reactive power of a plural-phase power line, wherein said step of using the digital computer to calculate each said electrical parameter comprises the substeps of:

for each phase, phase-shifting by ninety degrees the digitized response to signal from said voltage sensing apparatus for that phase, after it has been corrected for non-linearities and gain errors and has been high-pass digitally filtered, thereby to generate a digital quadrature voltage response for that phase;

for each phase, multiplying the digital quadrature voltage response for that phase by the digitized response to signal from said current sensing apparatus for that phase, after it has been corrected for non-linearities and gain errors, has been high-pass digitally filtered and has been phase-corrected, thereby to generate a respective digital product signal for that phase;

adding together the respective digital product signals for all the phases to generate a digital sum signal; and

low-pass digitally filtering the digital sum signal to generate a low-pass filter response that corresponds to a calculation of the reactive power of the plural-phase power line.

17. The method of claim 12, employed for measuring the apparent power of a single power line phase, wherein said step of using the digital computer to calculate each said electrical parameter comprises the substeps of:

multiplying the digitized response to signal from said voltage sensing apparatus for said single power line phase, after it has been corrected for non-linearities and gain errors and has been high-pass digitally filtered, by the digitized response to signal from said current sensing apparatus for said single power line phase, after it has been corrected for non-linearities and gain errors, has been high-pass digitally filtered and has been phase-corrected, thereby to generate a first digital product signal;

low-pass digitally filtering the first digital product signal to generate a first low-pass filter response that corresponds to a calculation of the real power for said single power line phase;

phase-shifting by ninety degrees the digitized response to signal from said voltage sensing apparatus for said single power line phase, after it has been corrected for non-linearities and gain errors and has been high-pass digitally filtered, thereby to generate a digital quadrature voltage response;

multiplying the digital quadrature voltage response by the digitized response to signal from said current sensing apparatus for said single power line phase, after it has been corrected for non-linearities and gain errors, has been high-pass digitally filtered and has been phase-corrected, thereby to generate a second digital product signal;

low-pass digitally filtering the digital product signal to generate a second low-pass filter response that corresponds to a calculation of the reactive power for said single power line phase; and

generating the vector sum of said first and second low-pass filter responses, that corresponds to a calculation of the apparent power for said single power line phase.

18. The method of claim 17 wherein said step of generating the vector sum of said first and second low-pass filter responses is carried out using a CORDIC procedure.

19. The method of claim 17, being employed for measuring the power factor of a single power line phase and including the further step of:

dividing said first low-pass filter response by said vector sum of said first and second low-pass filter responses, thereby to calculate the power factor for said single power line phase.

20. The method of claim 12, employed for measuring the apparent power of a plural-phase power line, wherein said step of using the digital computer to calculate each said electrical parameter comprises the substeps of:

for each phase, multiplying the digitized response to signal from said voltage sensing apparatus for that phase, after it has been corrected for non-linearities and gain errors and has been high-pass digitally filtered, by the digitized response to signal from said current sensing apparatus for that phase, after it has been corrected for non-linearities and gain errors, has been high-pass digitally filtered and has been phase-corrected, thereby to generate a respective first digital product signal for that phase;

adding together the respective first digital product signals for all the phases to generate a first digital sum signal;

low-pass digitally filtering the first digital sum signal to generate a first low-pass filter response that corresponds to a calculation of the real power of the plural-phase power line;

for each phase, phase-shifting by ninety degrees the digitized response to signal from said voltage sensing apparatus for that phase, after it has been corrected for non-linearities and gain errors and has been high-pass digitally filtered, thereby to generate a digital quadrature voltage response for that phase;

for each phase, multiplying the digital quadrature voltage response for that phase by the digitized response to signal from said current sensing apparatus for that phase, after it has been corrected for non-linearities and gain errors, has been high-pass digitally filtered and has been phase-corrected, thereby to generate a respective second digital product signal for that phase;

adding together the respective second digital product signals for all the phases to generate a second digital sum signal; and

low-pass digitally filtering the second digital sum signal to generate a second low-pass filter response that corresponds to a calculation of the reactive power of the plural-phase power line; and

generating the vector sum of said first and second low-pass filter responses, that corresponds to a calculation of the apparent power of the plural-phase power line.

21. The method of claim 20 wherein said step of generating the vector sum of said first and second low-pass filter responses is carried out using a CORDIC procedure.

22. The method of claim 20, being employed for measuring the power factor of a plural-phase power line and including the further step of:

dividing said first low-pass filter response by said vector sum of said first and second low-pass filter responses, thereby to calculate the power factor of said plural-phase power line.

23. The method of claim 12, employed for measuring the phase angle of a single power line phase, wherein said step of using the digital computer to calculate each said electrical parameter comprises the substeps of:

multiplying the digitized response to signal from said voltage sensing apparatus for said single power line phase, after it has been corrected for non-linearities and gain errors and has been high-pass digitally filtered, by the digitized response to signal from said current sensing apparatus for said single power line phase, after it has been corrected for non-linearities and gain errors, has been high-pass digitally filtered and has been phase-corrected, thereby to generate a first digital product signal;

low-pass digitally filtering the first digital product signal to generate a first low-pass filter response that corresponds to a calculation of the real power for said single power line phase;

phase-shifting by ninety degrees the digitized response to signal from said voltage sensing apparatus for said single power line phase, after it has been corrected for non-linearities and gain errors and has been high-pass digitally filtered, thereby to generate a digital quadrature voltage response;

multiplying the digital quadrature voltage response by the digitized response to signal from said current sensing apparatus for said single power line phase, after it has been corrected for non-linearities and gain errors, has been high-pass digitally filtered and has been phase-corrected, thereby to generate a second digital product signal;

low-pass digitally filtering the digital product signal to generate a second low-pass filter response that corresponds to a calculation of the reactive power for said single power line phase; and

calculating the angle between said first and second low-pass filter responses, which corresponds to the phase angle for said single power line phase.

24. The method of claim 23 wherein said step of calculating the angle between said first and second low-pass filter responses is carried out using a CORDIC procedure.

25. The method of claim 12, employed for measuring the phase angle of a plural-phase power line, wherein said step of using the digital computer to calculate each said electrical parameter comprises the substeps of:

for each phase, multiplying the digitized response to signal from said voltage sensing apparatus for that phase, after it has been corrected for non-linearities and gain errors and has been high-pass digitally filtered, by the digitized response to signal from said current sensing apparatus for that phase, after it has been corrected for non-linearities and gain errors, has been high-pass digitally filtered and has been phase-corrected, thereby to generate a respective first digital product signal for that phase;

adding together the respective first digital product signals for all the phases to generate a first digital sum signal; and

low-pass digitally filtering the first digital sum signal to generate a first low-pass filter response that corresponds to a calculation of the real power of the plural-phase power line.

for each phase, phase-shifting by ninety degrees the digitized response to signal from said voltage sensing apparatus for that phase, after it has been corrected for non-linearities and gain errors and has been high-pass digitally filtered, thereby to generate a digital quadrature voltage response for that phase;

for each phase, multiplying the digital quadrature voltage response for that phase by the digitized response to signal from said current sensing apparatus for that phase, after it has been corrected for non-linearities and gain errors, has been high-pass digitally filtered and has been phase-corrected, thereby to generate a respective second digital product signal for that phase;

adding together the respective second digital product signals for all the phases to generate a second digital sum signal; and

low-pass digitally filtering the second digital sum signal to generate a second low-pass filter response that corresponds to a calculation of the reactive power of the plural-phase power line; and

calculating the angle between said first and second low-pass filter responses, which corresponds to the phase angle of the plural-phase power line.

26. The method of claim 25 wherein said step of calculating the angle between said first and second low-pass filter responsed is carried out using a CORDIC procedure.

27. The method of claim 11, employed for measuring the real power of a single power line phase, wherein said step of using the digital computer to calculate each said electrical parameter comprises the substeps of:

multiplying the digitized response to signal from said voltage sensing apparatus for said single power line phase, after it has been corrected for non-linearities and gain errors and has been high-pass digitally filtered, by the digitized response to signal from said current sensing apparatus for said single power line phase, after it has been corrected for non-linearities and gain errors, has been high-pass digitally filtered and has been phase-corrected, thereby to generate a digital product signal; and

low-pass digitally filtering the digital product signal to generate a low-pass filter response that corresponds to a calculation of the real power for said single power line phase.

28. The method of claim 11, employed for measuring the real power of a plural-phase power line, wherein said step of using the digital computer to calculate each said electrical parameter comprises the substep of:

for each phase, multiplying the digitized response to signal from said voltage sensing apparatus for that phase, after it has been corrected for non-linearities and gain errors and has been high-pass digitally filtered, by the digitized response to signal from said current sensing apparatus for that phase, after it has been corrected for non-linearities and gain errors, has been high-pass digitally filtered and has been phase-corrected, thereby to generate a respective digital product signal for that phase;

adding together the respective digital product signals for all the phases to generate a digital sum signal; and

low-pass digitally filtering the digital sum signal to generate a low-pass filter response that corresponds to a calculation of the real power of the plural-phase power line.

29. The method of claim 11, employed for measuring the reactive power of a single power line phase, wherein said step of using the digital computer to calculate each said electrical parameter comprises the substeps of:

phase-shifting by ninety degrees the digitized response to signal from said voltage sensing apparatus for said single power line phase, after it has been corrected for non-linearities and gain errors and has been high-pass digitally filtered, thereby to generate a digital quadrature voltage response;

multiplying the digital quadrature voltage response by the digitized response to signal from said current sensing apparatus for said single power line phase, after it has been corrected for non-linearities and gain errors, has been high-pass digitally filtered and has been phase-corrected, thereby to generate a digital product signal; and

low-pass digitally filtering the digital product signal to generate a low-pass filter response that corresponds to a calculation of the reactive power for said single power line phase.

30. The method of claim 11, employed for measuring the reactive power of a plural-phase power line, wherein said step of using the digital computer to calculate each said electrical parameter comprises the substeps of:

for each phase, phase-shifting by ninety degrees the digitized response to signal from said voltage sensing apparatus for that phase, after it has been corrected for non-linearities and gain errors and has been high-pass digitally filtered, thereby to generate a digital quadrature voltage response for that phase;

for each phase, multiplying the digital quadrature voltage response for that phase by the digitized response to signal from said current sensing apparatus for that phase, after it has been corrected for non-linearities and gain errors, has been high-pass digitally filtered and has been phase-corrected, thereby to generate a respective digital product signal for that phase;

adding together the respective digital product signals for all the phases to generate a digital sum signal; and

low-pass digitally filtering the digital sum signal to generate a low-pass filter response that corresponds to a calculation of the reactive power of the plural-phase power line.

31. The method of claim 11, employed for measuring the apparent power of a single power line phase, wherein said step of using the digital computer to calculate each said electrical parameter comprises the substeps of:

multiplying the digitized response to signal from said voltage sensing apparatus for said single power line phase, after it has been corrected for non-linearities and gain errors and has been high-pass digitally filtered, by the digitized response to signal from said current sensing apparatus for said single power line phase, after it has been corrected for non-linearities and gain errors, has been high-pass digitally filtered and has been phase-corrected, thereby to generate a first digital product signal;

low-pass digitally filtering the first digital product signal to generate a first low-pass filter response that corresponds to a calculation of the real power for said single power line phase;

phase-shifting by ninety degrees the digitized response to signal from said voltage sensing apparatus for said single power line phase, after it has been corrected for non-linearities and gain errors and has been high-pass digitally filtered, thereby to generate a digital quadrature voltage response;

multiplying the digital quadrature voltage response by the digitized response to signal from said current sensing apparatus for said single power line phase, after it has been corrected for non-linearities and gain errors, has been high-pass digitally filtered and has been phase-corrected, thereby to generate a second digital product signal;

low pass digitally filtering the digital product signal to generate a second low-pass filter response that corresponds to a calculation of the reactive power for said single power line phase; and

generating the vector sum of said first and second low-pass filter responses, that corresponds to a calculation of the apparent power for said single power line phase.

32. The method of claim 31, being employed for measuring the power factor for said single power line phase and including the further step of:

dividing said first low-pass filter response by said vector sum of said first and second low-pass filter responses, thereby to calculate the power factor of said single-phase power line.

33. The method of claim 11, employed for measuring the apparent power of a plural-phase power line, wherein said step of using the digital computer to calculate each said electrical parameter comprises the substeps of:

for each phase, multiplying the digitized response to signal from said voltage sensing apparatus for that phase, after it has been corrected for non-linearities and gain errors and has been high-pass digitally filtered, by the digitized response to signal from said current sensing apparatus for that phase, after it has been corrected for non-linearities and gain errors, has been high-pass digitally filtered and has been phase-corrected, thereby to generate a respective first digital product signal for that phase;

adding together the respective first digital product signals for all the phases to generate a first digital sum signal; and

low-pass digitally filtering the first digital sum signal to generate a first low-pass filter response that corresponds to a calculation of the real power of the plural-phase power line.

for each phase, phase-shifting by ninety degrees the digitized response to signal from said voltage sensing apparatus for that phase, after it has been corrected for non-linearities and gain errors and has been high-pass digitally filtered, thereby to generate a digital quadrature voltage response for that phase;

for each phase, multiplying the digital quadrature voltage response for that phase by the digitized response to signal from said current sensing apparatus for that phase, after it has been corrected for non-linearities and gain errors, has been high-pass digitally filtered and has been phase-corrected, thereby to generate a respective second digital product signal for that phase;

adding together the respective second digital product signals for all the phases to generate a second digital sum signal; and

low-pass digitally filtering the second digital sum signal to generate a second low-pass filter response that corresponds to a calculation of the reactive power of the plural-phase power line; and

generating the vector sum of said first and second low-pass filter responses, that corresponds to a calculation of the apparent power of the plural-phase power line.

34. The method of claim 33, being employed for measuring the power factor of a plural-phase power line and including the further step of:

dividing said first low-pass filter response by said vector sum of said first and second low-pass filter responses, thereby to calculate the power factor of said plural-phase power line.

35. The method of claim 11, employed for measuring the phase angle of a single power line phase, wherein said step of using the digital computer to calculate each said electrical parameter comprises the substeps of:

multiplying the digitized response to signal from said voltage sensing apparatus for said single power line phase, after it has been corrected for non-linearities and gain errors and has been high-pass digitally filtered, by the digitized response to signal from said current sensing apparatus for said single power line phase, after it has been corrected for non-linearities and gain errors, has been high-pass digitally filtered and has been phase-corrected, thereby to generate a first digital product signal;

low-pass digitally filtering the first digital product signal to generate a first low-pass filter response that corresponds to a calculation of the real power for said single power line phase;

phase-shifting by ninety degrees the digitized response to signal from said voltage sensing apparatus for said single power line phase, after it has been corrected for non-linearities and gain errors and has been high-pass digitally filtered, thereby to generate a digital quadrature voltage response;

multiplying the digital quadrature voltage response by the digitized response to signal from said current sensing apparatus for said single power line phase, after it has been corrected for non-linearities and gain errors, has been high-pass digitally filtered and has been phase-corrected, thereby to generate a second digital product signal;

low-pass digitally filtering the digital product signal to generate a second low-pass filter response that corresponds to a calculation of the reactive power for said single power line phase; and

calculating the angle between said first and second low-pass filter responses, which corresponds to the phase angle for said single power line phase.

36. The method of claim 11, employed for measuring the phase angle of a plural-phase power line, wherein said step of using the digital computer to calculate each said electrical parameter comprises the substeps of:

for each phase, multiplying the digitized response to signal from said voltage sensing apparatus for that phase, after it has been corrected for non-linearities and gain errors and has been high-pass digitally filtered, by the digitized response to signal from said current sensing apparatus for that phase, after it has been corrected for non-linearities and gain errors, has been high-pass digitally filtered and has been phase-corrected, thereby to generate a respective first digital product signal for that phase;

adding together the respective first digital product signals for all the phases to generate a first digital sum signal; and

low-pass digitally filtering the first digital sum signal to generate a first low-pass filter response that corresponds to a calculation of the real power of the plural-phase power line.

for each phase, phase-shifting by ninety degrees the digitized response to signal from said voltage sensing apparatus for that phase, after it has been corrected for non-linearities and gain errors and has been high-pass digitally filtered, thereby to generate a digital quadrature voltage response for that phase;

for each phase, multiplying the digital quadrature voltage response for that phase by the digitized response to signal from said current sensing apparatus for that phase, after it has been corrected for non-linearities and gain errors, has been high-pass digitally filtered and has been phase-corrected, thereby to generate a respective second digital product signal for that phase;

adding together the respective second digital product signals for all the phases to generate a second digital sum signal; and

low-pass digitally filtering the second digital sum signal to generate a second low-pass filter response that corresponds to a calculation of the reactive power of the plural-phase power line; and

calculating the angle between said first and second low-pass filter responses, which corresponds to the phase angle of the plural-phase power line.

37. The method of claim 11 including the additional step of:

supplying a calculated electrical parameter from said digital computer to apparatus generating indications of the calculated electrical parameter of a form perceptible to a human being.

38. The method of claim 37 wherein the additional step of supplying a calculated electrical parameter from said digital computer to apparatus generating indications of the calculated electrical parameter of a form perceptible to a human being comprises applying the calculated electrical parameter to a digital read-out device.

39. The method of claim 37 wherein the additional step of supplying a calculated electrical parameter from said digital computer to apparatus generating indications of the calculated electrical parameter of a form perceptible to a human being comprises the substeps of:

using a pulse-duration modulator to generate pulses having a duration directly related to the calculated electrical parameter from said digital computer; and

applying the pulses to a D'"'"'Arsonval meter.

40. A method for measuring at least one electrical parameter of the operation of a p-phase power line, p being a positive integer, said method comprising the steps of:

arranging respective sensing apparatus to sense at least one of the voltages and currents associated with each phase of said power line;

using analog-to-digital conversion apparatus to digitize simultaneously the response of each sensing apparatus, thereby to generate corresponding digital responses;

using a digital computer to correct each digitized response of said analog-to-digital conversion apparatus for non-linearities and gain errors in the responses of said sensing apparatus and said analog-to-digital conversion apparatus;

using the digital computer to high-pass digitally filter each digital response that has been corrected for non-linearities and gain errors, in order to suppress any attendant direct term;

using the digital computer to calculate the frequency of a digital response that has been corrected for non-linearities and gain errors and has been high-pass digitally filtered;

using the digital computer to respond to the calculated frequency to further correct each digitized response of said analog-to-digital conversion apparatus for non-linearities and gain errors;

using the digital computer to high-pass digitally filter each digital response that has been further corrected for non-linearities and gain errors, in order to suppress attendant direct terms; and

using the digital computer to calculate each said electrical parameter, proceeding from each digital response that has been further corrected for non-linearities and gain errors and has been high-pass digitally filtered.

41. A method for measuring at least one electrical parameter of the operation of a p-phase power line, p being a positive integer, said method comprising the steps of:

arranging respective current sensing apparatus to sense the analog current flow in each phase of said power line;

arranging respective voltage sensing apparatus to sense the analog voltage across each phase of said power line;

using analog-to-digital conversion apparatus to digitize simultaneously the response of each current sensing apparatus and of each voltage sensing apparatus, thereby to generate corresponding digital responses;

using a digital computer to correct the digitized responses of said analog-to-digital conversion apparatus for non-linearities and gain errors in the responses of said current sensing apparatus and said voltage sensing apparatus and said analog-to-digital conversion apparatus;

using the digital computer to high-pass digitally filter the digital responses that have been corrected for non-linearities and gain errors, in order to suppress attendant direct terms;

using the digital computer to calculate the frequency of the digital responses that have been corrected for non-linearities and gain errors and have been high-pass digitally filtered;

using the digital computer to respond to the calculated frequency to further correct the digitized responses of said analog-to-digital conversion apparatus for non-linearities and gain errors in the responses of said current sensing apparatus and said voltage sensing apparatus and said analog-to-digital conversion apparatus;

using the digital computer to high-pass digitally filter the digital responses that have been further corrected for non-linearities and gain errors, in order to suppress attendant direct terms;

using the digital computer to respond to the calculated frequency to generate phase corrections of the digital responses that have been further corrected for non-linearities and gain errors and have been high-pass digitally filtered; and

using the digital computer to calculate each said electrical parameter, proceeding from the digital responses that have been further corrected for non-linearities and gain errors, have been high-pass digitally filtered, and have been phase-corrected.

42. A method for measuring at least one electrical parameter of the operation of a p-phase power line having a respective conductor for each phase, p being at least three, said method comprising the steps of:

arranging respective current sensing apparatus to sense the analog current flow in each phase of said power line except a first phase appearing on a first of said p conductors;

arranging respective voltage sensing apparatus to sense the analog voltage of each phase of said power line except said first phase, respective to the voltage appearing on said first conductor;

using analog-to-digital conversion apparatus to digitize the response of each current sensing apparatus and of each voltage sensing apparatus, thereby to generate corresponding digital responses;

using a digital computer to correct the digitized responses of said analog-to-digital conversion apparatus for non-linearities and gain errors in the responses of said current sensing apparatus and said voltage sensing apparatus and said analog-to-digital conversion apparatus;

using the digital computer to high-pass digitally filter the digital responses that have been corrected for non-linearities and gain errors, in order to suppress attendant direct terms;

using the digital computer to calculate the frequency of one of the digital responses that has been corrected for non-linearities and gain errors and has been high-pass digitally filtered;

using the digital computer to respond to the calculated frequency to generate a phase correction of the digital response to each current sensing apparatus that has been corrected for non-linearities and gain errors and has been high-pass digitally filtered; and

using the digital computer to calculate each said electrical parameter, proceeding from the digital responses that have been corrected for non-linearities and gain errors, have been high-pass digitally filtered, and have been phase-corrected.

43. The method of claim 42 wherein said step of using the digital computer to calculate each said electrical parameter includes substeps of:

low-pass digitally filtering to generate a low-pass filter response, and

generating the kernel for said substep of low-pass digitally filtering with a width determined from said calculated frequency to extend over an integral number of cycles of said electrical parameter.

44. The method of claim 43 for measuring the real power of said p-phase power line, wherein said step of using the digital computer to calculate each said electrical parameter comprises the substeps of:

for each phase except said first, multiplying the digitized response to signal from said voltage sensing apparatus for that phase, after it has been corrected for non-linearities and gain errors and has been high-pass digitally filtered, by the digitized response to signal from said current sensing apparatus for that phase, after it has been corrected for non-linearities and gain errors, has been high-pass digitally filtered and has been phase-corrected, thereby to generate a respective digital product signal for that phase;

adding together the respective digital product signals for all the phases except said first to generate a digital sum signal;

multiplying said digital sum signal by a weighting factor; and

low-pass digitally filtering the resulting weighted digital sum signal to generate a low-pass filter response that corresponds to a calculation of the real power of the plural-phase power line.

45. The method of claim 43 for measuring the reactive power of said p-phase power line, wherein said step of using the digital computer to calculate each said electrical parameter comprises the substeps of:

for each phase except said first, phase-shifting by ninety degrees the digitized response to signal from said voltage sensing apparatus for that phase, after it has been corrected for non-linearities and gain errors and has been high-pass digitally filtered, thereby to generate a digital quadrature voltage response for that phase;

for each phase except said first, multiplying the digital quadrature voltage response for that phase by the digitized response to signal from said current sensing apparatus for that phase, after it has been corrected for non-linearities and gain errors, has been high-pass digitally filtered and has been phase-corrected, thereby to generate a respective digital product signal for that phase;

adding together the respective digital product signals for all the phases to generate a digital sum signal;

multiplying said digital sum signal by a weighting factor; and

low-pass digitally filtering the resulting weighted digital sum signal to generate a low-pass filter response that corresponds to a calculation of the reactive power of the plural-phase power line.

46. The method of claim 43 for measuring the apparent power of said p-phase power line, wherein said step of using the digital computer to calculate each said electrical parameter comprises the substeps of:

for each phase except said first, multiplying the digitized response to signal from said voltage sensing apparatus for that phase, after it has been corrected for non-linearities and gain errors and has been high-pass digitally filtered, by the digitized response to signal from said current sensing apparatus for that phase, after it has been corrected for non-linearities and gain errors, has been high-pass digitally filtered and has been phase-corrected, thereby to generate a respective first digital product signal for that phase;

adding together the respective first digital product signals for all the phases except said to generate a first digital sum signal;

multiplying said first digital sum signal by a first weighting factor;

low-pass digitally filtering the resulting weighted first digital sum signal to generate a first low-pass filter response that corresponds to a calculation of the real power of the plural-phase power line;

for each phase except said first, phase-shifting by ninety degrees the digitized response to signal from said voltage sensing apparatus for that phase, after it has been corrected for non-linearities and gain errors and has been high-pass digitally filtered, thereby to generate a digital quadrature voltage response for that phase;

for each phase except said first, multiplying the digital quadrature voltage response for that phase by the digitized response to signal from said current sensing apparatus for that phase, after it has been corrected for non-linearities and gain errors, has been high-pass digitally filtered and has been phase-corrected, thereby to generate a respective second digital product signal for that phase;

adding together the respective second digital product signals for all the phases except said first to generate a second digital sum signal;

multiplying said second digital sum signal by a second weighting factor;

low-pass digitally filtering the resulting weighted second digital sum signal to generate a second low-pass filter response that corresponds to a calculation of the reactive power of the plural-phase power line; and

generating the vector sum of said first and second low-pass filter responses, that corresponds to a calculation of the apparent power of the plural-phase power line.

47. The method of claim 46 wherein said step of generating the vector sum of said first and second low-pass filter responses is carried out using a CORDIC procedure.

48. The method of claim 46, being employed for measuring the power factor of said p-phase power line and including the further step of:

dividing said first low-pass filter response by said vector sum of said first and second low-pass filter responses, thereby to calculate the power factor of said plural-phase power line.

49. The method of claim 43, employed for measuring the phase angle of said p-phase power line, wherein said step of using the digital computer to calculate each said electrical parameter comprises the substeps of:

for each phase except said first, multiplying the digitized response to signal from said voltage sensing apparatus for that phase, after it has been corrected for non-linearities and gain errors and has been high-pass digitally filtered, by the digitized response to signal from said current sensing apparatus for that phase, after it has been corrected for non-linearities and gain errors, has been high-pass digitally filtered and has been phase-corrected, thereby to generate a respective first digital product signal for that phase;

adding together the respective first digital product signals for all the phases except said first to generate a first digital sum signal;

multiplying said first digital sum signal by a first weighting factor;

low-pass digitally filtering the resulting weighted first digital sum signal to generate a first low-pass filter response that corresponds to a calculation of the the real power of the plural-phase power line;

for each phase, phase-shifting by ninety degrees the digitized response to signal from said voltage sensing apparatus for that phase, after it has been corrected for non-linearities and gain errors and has been high-pass digitally filtered, thereby to generate a digital quadrature voltage response for that phase;

for each phase, multiplying the digital quadrature voltage response for that phase by the digitized response to signal from said current sensing apparatus for that phase, after it has been corrected for non-linearities and gain errors, has been high-pass digitally filtered and has been phase-corrected, thereby to generate a respective second digital product signal for that phase;

adding together the respective second digital product signals for all the phases to generate a second digital sum signal;

multiplying said second digital sum signal by a second weighting factor;

low-pass digitally filtering the resulting weighted second digital sum signal to generate a second low-pass filter response that corresponds to a calculation of the reactive power of the plural-phase power line; and

calculating the angle between said first and second low-pass filter responses, which corresponds to the phase angle of the plural-phase power line.

50. The method of claim 49 wherein said step of calculating the angle between said first and second low-pass filter responses is carried out using a CORDIC procedure.

51. The method of claim 42 for measuring the real power of said p-phase power line, wherein said step of using the digital computer to calculate each said electrical parameter comprises the substeps of:

for each phase except said first, multiplying the digitized response to signal from said voltage sensing apparatus for that phase, after it has been corrected for non-linearities and gain errors and has been high-pass digitally filtered, by the digitized response to signal from said current sensing apparatus for that phase, after it has been corrected for non-linearities and gain errors, has been high-pass digitally filtered and has been phase-corrected, thereby to generate a respective digital product signal for that phase;

adding together the respective digital product signals for all the phases except said first to generate a digital sum signal;

multiplying said digital sum signal by a weighting factor; and

low-pass digitally filtering the resulting weighted digital sum signal to generate a low-pass filter response that corresponds to a calculation of the real power of the plural-phase power line.

52. The method of claim 42 for measuring the reactive power of said p-phase power line, wherein said step of using the digital computer to calculate each said electrical parameter comprises the substeps of:

for each phase except said first, phase-shifting by ninety degrees the digitized response to signal from said voltage sensing apparatus for that phase, after it has been corrected for non-linearities and gain errors and has been high-pass digitally filtered, thereby to generate a digital quadrature voltage response for that phase;

for each phase except said first, multiplying the digital quadrature voltage response for that phase by the digitized response to signal from said current sensing apparatus for that phase, after it has been corrected for non-linearities and gain errors, has been high-pass digitally filtered and has been phase-corrected, thereby to generate a respective digital product signal for that phase;

adding together the respective digital product signals for all the phases to generate a digital sum signal;

multiplying said digital sum signal by a weighting factor; and

low-pass digitally filtering the resulting weighted digital sum signal to generate a low-pass filter response that corresponds to a calculation of the reactive power of the plural-phase power line.

53. The method of claim 42 for measuring the apparent power of said p-phase power line, wherein said step of using the digital computer to calculate each said electrical parameter comprises the substeps of:

for each phase except said first, multiplying the digitized response to signal from said voltage sensing apparatus for that phase, after it has been corrected for non-linearities and gain errors and has been high-pass digitally filtered, by the digitized response to signal from said current sensing apparatus for that phase, after it has been corrected for non-linearities and gain errors, has been high-pass digitally filtered and has been phase-corrected, thereby to generate a respective first digital product signal for that phase;

adding together the respective first digital product signals for all the phases except said to generate a first digital sum signal;

multiplying said first digital sum signal by a first weighting factor;

low-pass digitally filtering the resulting weighted first digital sum signal to generate a first low-pass filter response that corresponds to a calculation of the real power of the plural-phase power line;

for each phase except said first, phase-shifting by ninety degrees the digitized response to signal from said voltage sensing apparatus for that phase, after it has been corrected for non-linearities and gain errors and has been high-pass digitally filtered, thereby to generate a digital quadrature voltage response for that phase;

for each phase except said first, multiplying the digital quadrature voltage response for that phase by the digitized response to signal from said current sensing apparatus for that phase, after it has been corrected for non-linearities and gain errors, has been high-pass digitally filtered and has been phase-corrected, thereby to generate a respective second digital product signal for that phase;

adding together the respective second digital product signals for all the phases except said first to generate a second digital sum signal;

multiplying said second digital sum signal by a second weighting factor;

low-pass digitally filtering the resulting weighted second digital sum signal to generate a second low-pass filter response that corresponds to a calculation of the reactive power of the plural-phase power line; and

generating the vector sum of said first and second low-pass filter responses, that corresponds to a calculation of the apparent power of the plural-phase power line.

54. The method of claim 53, being employed for measuring the power factor of said p-phase power line and including the further step of:

dividing said first low-pass filter response by said vector sum of said first and second low-pass filter responses, thereby to calculate the power factor of said plural-phase power line.

55. The method of claim 42, employed for measuring the phase angle of said p-phase power line, wherein said step of using the digital computer to calculate each said electrical parameter comprises the substeps of:

for each phase except said first, multiplying the digitized response to signal from said voltage sensing apparatus for that phase, after it has been corrected for non-linearities and gain errors and has been high-pass digitally filtered, by the digitized response to signal from said current sensing apparatus for that phase, after it has been corrected for non-linearities and gain errors, has been high-pass digitally filtered and has been phase-corrected, thereby to generate a respective first digital product signal for that phase;

adding together the respective first digital product signals for all the phases except said first to generate a first digital sum signal;

multiplying said first digital sum signal by a first weighting factor;

low-pass digitally filtering the resulting weighted first digital sum signal to generate a first low-pass filter response that corresponds to a calculation of the real power of the plural-phase power line;

for each phase, phase-shifting by ninety degrees the digitized response to signal from said voltage sensing apparatus for that phase, after it has been corrected for non-linearities and gain errors and has been high-pass digitally filtered, thereby to generate a digital quadrature voltage response for that phase;

for each phase, multiplying the digital quadrature voltage response for that phase by the digitized response to signal from said current sensing apparatus for that phase, after it has been corrected for non-linearities and gain errors, has been high-pass digitally filtered and has been phase-corrected, thereby to generate a respective second digital product signal for that phase;

adding together the respective second digital product signals for all the phases to generate a second digital sum signal;

multiplying said second digital sum signal by a second weighting factor;

low-pass digitally filtering the resulting weighted second digital sum signal to generate a second low-pass filter response that corresponds to a calculation of the reactive power of the plural-phase power line; and

calculating the angle between said first and second low-pass filter responses, which corresponds to the phase angle of the plural-phase power line.

56. The method of claim 42 including the additional step of:

supplying a calculated electrical parameter from said digital computer to apparatus generating indications of the calculated electrical parameter of a form perceptible to a human being.

57. The method of claim 56 wherein the additional step of supplying a calculated electrical parameter from said digital computer to apparatus generating indications of the calculated electrical parameter of a form perceptible to a human being comprises applying the calculated electrical parameter to a digital read-out device.

58. The method of claim 56 wherein the additional step of supplying a calculated electrical parameter from said digital computer to apparatus generating indications of the calculated electrical parameter of a form perceptible to a human being comprises the substeps of:

using a pulse-duration modulator to generate pulses having a duration directly related to the calculated electrical parameter from said digital computer; and

applying the pulses to a D'"'"'Arsonval meter.

59. A method for measuring at least one electrical parameter of the operation of a p-phase power line, p being an integer at least three, said method comprising the steps of:

arranging respective voltage sensing apparatus to sense the analog voltage of each phase of said power line except said first as referred to the analog voltage appearing on said first conductor;

using analog-to-digital conversion apparatus to digitize simultaneously the response of each voltage sensing apparatus, thereby to generate corresponding digital responses;

using a digital computer to correct each digitized response of said analog-to-digital conversion apparatus for non-linearities and gain errors in the responses of said voltage sensing apparatus and said analog-to-digital conversion apparatus;

using the digital computer to high-pass digitally filter each digital response that has been corrected for non-linearities and gain errors, in order to suppress any attendant direct term;

using the digital computer to calculate the frequency of a digital response that has been corrected for non-linearities and gain errors and has been high-pass digitally filtered;

using the digital computer to respond to the calculated frequency to further correct each digitized response of said analog-to-digital conversion apparatus for non-linearities and gain errors;

using the digital computer to high-pass digitally filter each digital response that has been further corrected for non-linearities and gain errors, in order to suppress attendant direct terms; and

using the digital computer to calculate each said electrical parameter, proceeding from each digital response that has been further corrected for non-linearities and gain errors and has been high-pass digitally filtered.

60. A method for measuring at least one electrical parameter of the operation of a p-phase power line having a respective conductor for each phase, p being an integer at least three, said method comprising the steps of:

arranging respective current sensing apparatus to sense the analog current flow in each phase of said power line except a first phase flowing through a first of said conductors;

arranging respective voltage sensing apparatus to sense the analog voltage of each phase of said power line except said first as referred to the analog voltage appearing on said first conductor;

using analog-to-digital conversion apparatus to digitize simultaneously the response of each current sensing apparatus and of each voltage sensing apparatus, thereby to generate corresponding digital responses;

using a digital computer to correct the digitized responses of said analog-to-digital conversion apparatus for non-linearities and gain errors in the responses of said current sensing apparatus and said voltage sensing apparatus and said analog-to-digital conversion apparatus;

using the digital computer to high-pass digitally filter the digital responses that have been corrected for non-linearities and gain errors, in order to suppress attendant direct terms;

using the digital computer to calculate the frequency of the digital responses that have been corrected for non-linearities and gain errors and have been high-pass digitally filtered;

using the digital computer to respond to the calculated frequency to further correct the digitized responses of said analog-to-digital conversion apparatus for non-linearities and gain errors in the responses of said current sensing apparatus and said voltage sensing apparatus and said analog-to-digital conversion apparatus;

using the digital computer to high-pass digitally filter the digital responses that have been further corrected for non-linearities and gain errors, in order to suppress attendant direct terms;

using the digital computer to respond to the calculated frequency to generate phase corrections of the digital responses that have been further corrected for non-linearities and gain errors and have been high-pass digitally filtered; and

using the digital computer to calculate each said electrical parameter, proceeding from the digital responses that have been further corrected for non-linearities and gain errors, have been high-pass digitally filtered, and have been phase-corrected.