Method and apparatus for measuring the frequency of a spectral line

• US 5,075,619 A
• Filed: 04/06/1990
• Issued: 12/24/1991
• Est. Priority Date: 04/06/1990
• Status: Expired due to Term

• Current Assignee: Tektronix Incorporated (Fortive Corp.)
• Original Assignee: Tektronix Incorporated (Fortive Corp.)
• Inventors: Said, Ahmed M. F.
• Primary Examiner(s): Wieder, Kenneth A.
• Assistant Examiner(s): Solis, Jose M.
• Application Number:
  US07/505,878
• Time in Patent Office: 627 Days
• Field of Search: 356/27, 364/572, 364/484, 364/485, 342/14, 342/16, 342/17, 333/167, 333/203, 324/77 E, 324/77 F, 324/77 C, 324/77 D
• US Class Current: 324/76.31
• CPC Class Codes: G01R 23/165 using filters

Abstract

A method and apparatus are disclosed, that is suitable for digital or analog spectrum analyzers, for accurately and rapidly ascertaining the frequency of a spectral line by determining its location from the response of two Gaussian shaped filters whose center frequencies bracket the frequency of the spectral line. The difference is taken between the amplitudes in decibels of the responses of the two Gaussian filters to the spectral line input signal. The frequency of the spectral line is then found from the linear relationship fx=delta-log-ampl.*c1+c2, where c1 is proportional to the square of the standard deviation of the Gaussian filters and inversely proportional to the difference between the center frequencies, f1 and f2, of the Gaussian filters times the logarithm of e, and where c2 is the midpoint between the center frequencies, f1 and f2, of the Gaussian filters, G1 and G2. Alternatively, a sweeping local oscillator output can be mixed with the signal containing the spectral line of unknown frequency and the resulting signal applied to one Gaussian filter at two different times to produce equivalent results. In this case, c1 is proportional to the square of the standard deviation of the Gaussian filter and inversely proportional to the difference between the local oscillator frequencies, f,LO+1 and f,LO+2, at times t1 and t2, times the logarithm of e, and c2 is the average of the local oscillator frequencies, f,LO+1 and f,LO+2, plus f, the center frequency of the Gaussian filter.

Claims

1. A method for rapidly and accurately determining the frequency, fx, of a spectral line comprising the steps of:

applying a signal containing the spectral line to at least two Gaussian filters having different center frequencies;

measuring the logarithmic amplitude of a response from each of the Gaussian filters to produce amplitudes log-ampl-1 and log-ampl-2, respectively;

taking the difference between log-ampl-1 and log-ampl-2 to produce a delta logarithmic amplitude, delta-log-ampl; and

determining the frequency of the spectral line from the relationship between the response from the Gaussian filters according to the linear relationship fx=delta-log-ampl*c1+c2, where c1 is proportional to the square of the standard deviation of the Gaussian filters and inversely proportional to the difference between the different center frequencies times the logarithm of e, and where c2 is the midpoint between the different center frequencies,

2. A method for rapidly and accurately determining the frequency, fx, of a spectral line using a single Gaussian filter having a center frequency comprising the steps of:

at a first time a signal containing the spectral line mixed with the output of a local oscillator at a first frequency to the single Gaussian filter;

measuring the logarithmic amplitude of a first response from the single Gaussian filter to produce a first amplitude;

applying at a second time a signal containing the spectral line mixed with the output of a local oscillator at a second frequency to the single Gaussian filter;

measuring the logarithmic amplitude of a second response from the single Gaussian filter to produce a second amplitude;

taking the difference between the first and second amplitudes to produce a delta logarithmic amplitude, delta-log-ampl; and

determining the frequency of the spectral line from the relationship between the two responses from the single Gaussian filter according to the linear relationship fx=delta-log-ampl*c1+c2, where c1 is proportional to the square of the standard deviation of the single Gaussian filter and inversely proportional to the difference between the first and second frequencies times the logarithm of e, and where c2 is the average of the first and second frequencies plus the center frequency.

3. A digital spectrum analyzer of the type having means for converting an analog signal to a series of digital numbers representing a time record of the signal and means for performing Discrete Fourier Transforms for operating on the time record of the signal to produce spectral data in an output of a plurality of filter bins, comprising:

means for producing Gaussian windows for shaping the output of the filter bins;

means for determining the logarithmic outputs of the filter bins; and

means for determining from the logarithmic outputs of two adjacent filter bins a frequency of a spectral line according to the linear relationship fx=delta-log-ampl*c1+c2, where fx is the frequency of the spectral line, delta-log-ampl is the difference between the logarithmic outputs of the two adjacent filter bins, c1 is proportional to the square of the standard deviation of the Gaussian windows and inversely proportional to the difference between the center frequencies of the Gaussian windows times the logarithm of e, and c2 is the midpoint between the center frequencies.

4. An apparatus for determining the frequency, fx, of a spectral line comprising:

a first Gaussian filter having a first center frequency that is lower than fx, having as input a signal containing the spectral line and producing a first amplitude output;

a second Gaussian filter having a second center frequency that is higher than fx, having as input a signal containing the spectral line and producing a second amplitude output;

means for producing logarithmic amplitudes from the first and second amplitude outputs;

means for taking the difference between the logarithmic amplitudes to produce a delta logarithmic amplitude, delta-log-ampl; and

means for determining the frequency of the spectral line from the relationship between the responses from the two Gaussian filters according to the linear relationship fx=delta-log-ampl*c1+c2, where c1 is proportional to the square of the standard deviation of the Gaussian filters and inversely proportional to the difference between the center frequencies times the logarithm of e, and where c2 is the midpoint between the center frequencies.

5. An apparatus for determining the frequency, fx, of a spectral line comprising:

a sweeping local oscillator for producing an output frequency that varies with time such that the output frequency is a first frequency at a first time and a second frequency at a second time;

means for frequency mixing a signal containing the spectral line with the output frequency to produce an intermediate frequency;

a Gaussian filter having a center frequency, having as input the intermediate frequency and having as an output an amplitude signal;

logarithmic amplitude producing means to produce from the output of the Gaussian filter logarithmic amplitude signals at the first and second times, respectively;

means for taking the difference between the logarithmic amplitude signals to produce a delta logarithmic amplitude signal, delta-log-ampl; and

means for determining the frequency of the spectral line from the relationship between the responses from the Gaussian filter at the first and second times according to the linear relationship fx=delta-log-ampl*c1=c2, where c1 is proportional to the square of the standard deviation of the Gaussian filter and inversely proportional to the difference between the first and second frequencies times the logarithm of e, and where c2 is the average of the first and second frequencies, plus the center frequency of the Gaussian filter.