METHODS, DEVICES, AND PROGRAMS FOR DESIGNING A DIGITAL FILTER AND FOR GENERATING A NUMERICAL SEQUENCE OF DESIRED FREQUENCY CHARACTERISTICS

• US 20070067377A1
• Filed: 10/17/2006
• Published: 03/22/2007
• Est. Priority Date: 04/19/2004
• Status: Abandoned Application

• Current Assignee: NSC Company Limited (Nexon Co Ltd)
• Original Assignee: Neuro Solution Corp.
• Inventors: KOYANAGI, Yukio
• Application Number:
  US11/550,345
• Publication Number:
  US 20070067377A1
• Time in Patent Office: Days
• US Class Current: 708/300
• CPC Class Codes: H03H 17/06 Non-recursive filters
• CPC Class Codes: H03H 2017/0072 Theoretical filter design

Abstract

A standard function is inputted and an interpolation function of finite length is calculated therefrom. Then, the frequency characteristics of the interpolation function is shifted by a desired amount in the frequency axis direction, thereby determining input frequency characteristics based on specification. Filter coefficients are determined by performing inverse FFT of a numerical sequence representative of the input frequency characteristics and rounding is performed according to the coefficient values in order to obtain a smaller number of filter coefficients. Thus, it is possible to eliminate the need for windowing as an operation for decreasing the number of filter coefficients and easily design an FIR filter having desired frequency characteristics.

Claims

1-24. -24. (canceled)

25. A method of designing a digital filter of a type which multiplies data from taps of a tapped delay line comprising a plurality of lines, by respective coefficients and which adds up multiplication results for output, the method comprising:

a first step of inputting a standard function such that an impulse response from the standard function has a finite value other than zero only in a given area and a value of zero in all the other areas;

a second step of determining a ratio of a transition area indicative of an area of a predetermined part between a pass band and a stop band of a frequency amplitude characteristic determined by the standard function input in the first step, to the entire area indicative of an area from the pass band to the stop band;

a third step of determining an interpolation function length indicative of the length of an effective area in a direction of a frequency axis of the frequency amplitude characteristic of an interpolation function to be determined, from the transition area ratio determined in the second step and the transition area width based on specifications for the filter to be designed;

a fourth step of using the interpolation function length determined in the third step and the standard function input in the first step to determine the interpolation function of a finite length which joins a maximum amplitude value at a predetermined frequency position of the frequency amplitude characteristic and a minimum amplitude value at a frequency position that is at a distance equal to the interpolation function length from the predetermined frequency position together, the interpolation function having a period shorter than the standard function by an amount corresponding to the interpolation function length;

a fifth step of shifting the frequency amplitude characteristic of the interpolation function determined in the fourth step by a desired amount in the direction of the frequency axis;

a sixth step of transforming the frequency amplitude characteristic of the interpolation function determined in the fifth step, into a laterally symmetric type to determine a numerical sequence indicative of the frequency amplitude characteristic corresponding to the specifications for the filter to be designed;

a seventh step of subjecting the numerical sequence determined in the sixth step to an inverse Fourier transformation and extracting real terms from a result of the inverse Fourier transformation;

an eighth step of rearranging a former half and a latter half of the numerical sequence comprising the real terms extracted in the seventh step; and

a ninth step of executing a rounding process of rounding lower several bits of data of predetermined bits in the numerical sequence calculated in the eighth step to reduce the bits,

wherein the numerical sequence obtained in the ninth step is determined to be the filter coefficients.

29. A computer readable medium containing computer code thereon which, when executed by a computer, implements a digital filter designing program that functions to carry out the method steps of claim 25.

31. An FIR type digital filter having, as filter coefficients, a numerical sequence calculated using the designing method according to claim 25.

26. A method of designing a digital filter of a type which multiplies data from taps of a tapped delay line comprising a plurality of lines, by respective coefficients and which adds up multiplication results for output, the method comprising:

a first step of inputting a standard function such that an impulse response from the standard function has a finite value other than zero only in a given area and a value of zero in all the other areas;

a second step of determining a ratio of a transition area indicative of that area of a frequency amplitude characteristic determined according to the specification for the filter to be designed which contains amplitude values except a maximum amplitude value and a minimum amplitude value, to a transition area indicative of that area of a frequency amplitude characteristic determined according to the standard function which contains amplitude values except a maximum amplitude value and a minimum amplitude value;

a third step of using the transition area ratio determined in the second step to determine a start point and an end point of the transition area of the frequency amplitude characteristic determined according to the specifications for the filter to be designed;

a fourth step of using the transition area ratio determined in the second step, the start point and the end point of the transition area determined in the third step, and the standard function input in the first step to determine an interpolation function of a finite length which joins the start point and the end point of the transition area together and which has a period shorter than the standard function by an amount corresponding to the transition area ratio;

a fifth step of transforming the frequency amplitude characteristic of the interpolation function determined in the fourth step, into a laterally symmetric type to determine a numerical sequence indicative of the frequency amplitude characteristic corresponding to the specifications for the filter to be designed;

a sixth step of subjecting the numerical sequence determined in the fifth step to an inverse Fourier transformation and extracting real terms from a result of the inverse Fourier transformation;

a seventh step of rearranging a former half and a latter half of the numerical sequence comprising the real terms extracted in the sixth step; and

an eighth step of executing a rounding process of rounding lower several bits of data of predetermined bits in the numerical sequence calculated in the seventh step to reduce the bits,

wherein the numerical sequence obtained in the eighth step is determined to be the filter coefficients.

38. A computer readable medium containing computer code thereon which, when executed by a computer, implements a digital filter designing program that functions to carry out the method steps of claim 26.

40. An FIR type digital filter having, as filter coefficients, a numerical sequence calculated using the designing method according to claim 26.

27. A device that designs a digital filter of a type which multiplies data from taps of a tapped delay line comprising a plurality of lines, by respective coefficients and which adds up multiplication results for output, the device comprising:

input means for inputting a standard function such that an impulse response from the standard function has a finite value other than zero only in a given area and a value of zero in all the other areas; and

calculation means for performing;

a first operation of determining a transition area ratio that is a ratio of a transition area indicative of an area of a predetermined part between a pass band and a stop band of a frequency amplitude characteristic determined by the standard function input in the first step, to the entire area indicative of an area from the pass band to the stop band,

a second operation of determining an interpolation function length indicative of the length of an effective area in a direction of a frequency axis of the frequency amplitude characteristic of an interpolation function to be determined, from the transition area ratio and the transition area width based on specifications for the filter to be designed,

a third operation of using the interpolation function length and the standard function to determine the interpolation function of a finite length which joins a maximum amplitude value at a predetermined frequency position of the frequency amplitude characteristic and a minimum amplitude value at a frequency position that is at a distance equal to the interpolation function length from the predetermined frequency position together, the interpolation function having a period shorter than the standard function by an amount corresponding to the interpolation function length,

a fourth operation of shifting the frequency amplitude characteristic of the interpolation function by a desired amount in the direction of the frequency axis,

a fifth operation of transforming the shifted frequency amplitude characteristic of the interpolation function into a laterally symmetric type to determine a numerical sequence indicative of the frequency amplitude characteristic corresponding to the specifications for the filter to be designed,

a sixth operation of subjecting the determined numerical sequence to an inverse Fourier transformation and extracting real terms from a result of the inverse Fourier transformation,

a seventh operation of rearranging a former half and a latter half of the numerical sequence comprising the extracted real terms, and

an eighth operation of executing a rounding process of rounding lower several bits of data of predetermined bits in the numerical sequence comprising the real terms to reduce the bits,

wherein the numerical sequence obtained by the eighth operation is determined to be the filter coefficients.

30. A computer readable medium containing computer code thereon which, when executed by a computer, carries out functions associated with said calculation means for performing recited in claim 27.

41. An FIR type digital filter having, as filter coefficients, a numerical sequence calculated using the designing device according to claim 27.

28. A device that designs a digital filter of a type which multiplies data from taps of a tapped delay line comprising a plurality of lines, by respective coefficients and which adds up multiplication results for output, the device comprising:

input means for inputting a standard function such that an impulse response from the standard function has a finite value other than zero only in a given area and a value of zero in all the other areas; and

calculation means for performing;

a first operation of determining a transition area ratio that is a ratio of a transition area indicative of that area of a frequency amplitude characteristic determined according to the specification for the filter to be designed which contains amplitude values except a maximum amplitude value and a minimum amplitude value, to a transition area indicative of that area of a frequency amplitude characteristic determined by the standard function which contains amplitude values except a maximum amplitude value and a minimum amplitude value,

a second operation of using the transition area ratio to determine a start point and an end point of the transition area of the frequency amplitude characteristic determined according to the specifications for the filter to be designed,

a third operation of using the transition area ratio, the start point and end point of the transition area, and the standard function to determine an interpolation function of a finite length which joins the start point and end point of the transition area together and which has a period shorter than the standard function by an amount corresponding to the transition area ratio,

a fourth operation of transforming the frequency amplitude characteristic of the interpolation function into a laterally symmetric type to determine a numerical sequence indicative of the frequency amplitude characteristic corresponding to the specifications for the filter to be designed,

a fifth operation of subjecting the determined numerical sequence to an inverse Fourier transformation and extracting real terms from a result of the inverse Fourier transformation,

a sixth operation of rearranging a former half and a latter half of the numerical sequence comprising the extracted real terms, and

a seventh operation of executing a rounding process of rounding lower several bits of data of predetermined bits in the numerical sequence comprising the real terms to reduce the bits,

wherein the numerical sequence obtained by the seventh operation is determined to be the filter coefficients.

39. A computer readable medium containing computer code thereon which, when executed by a computer, carries out functions associated with said calculation means for performing recited in claim 28.

42. An FIR type digital filter having, as filter coefficients, a numerical sequence calculated using the designing device according to claim 28.

32. A method of generating a numerical sequence indicative of a frequency characteristic corresponding to specifications for an FIR digital filter to be designed, the method comprising:

a first step of inputting a standard function such that an impulse response from the standard function has a finite value other than zero only in a given area and a value of zero in all the other areas;

a second step of determining a ratio of a transition area indicative of an area of a predetermined part between a pass band and a stop band of a frequency amplitude characteristic determined by the standard function input in the first step, to the entire area indicative of an area from the pass band to the stop band;

a third step of determining an interpolation function length indicative of the length of an effective area in a direction of a frequency axis of the frequency amplitude characteristic of an interpolation function to be determined, from the transition area ratio determined in the second step and the transition area width based on specifications for the FIR digital filter to be designed;

a fourth step of using the interpolation function length determined in the third step and the standard function input in the first step to determine the interpolation function of a finite length which joins a maximum amplitude value at a predetermined frequency position of the frequency amplitude characteristic and a minimum amplitude value at a frequency position that is at a distance equal to the interpolation function length from the predetermined frequency position together, the interpolation function having a period shorter than the standard function by an amount corresponding to the interpolation function length; and

a fifth step of shifting the frequency amplitude characteristic of the interpolation function determined in the fourth step by a desired amount in the direction of the frequency axis to determine a numerical sequence for a frequency amplitude characteristic corresponding to the specifications for the FIR digital filter to be designed.

36. A computer readable medium containing computer code thereon which, when executed by a computer, carries out functions that generate a numerical sequence for a desired frequency characteristic according to the method steps of claim 32.

33. A method of generating a numerical sequence indicative of a frequency characteristic corresponding to specifications for an FIR digital filter to be designed, the method comprising:

a first step of inputting a standard function such that an impulse response from the standard function has a finite value other than zero only in a given area and a value of zero in all the other areas;

a second step of determining a transition area ratio that is a ratio of a transition area indicative of that area of a frequency amplitude characteristic determined according to the specifications for the FIR digital filter to be designed which contains amplitude values except a maximum amplitude value and a minimum amplitude value, to a transition area indicative of that area of a frequency amplitude characteristic determined by the standard function which contains amplitude values except a maximum amplitude value and a minimum amplitude value;

a third step of using the transition area ratio determined in the second step to determine a start point and an end point of the transition area of the frequency amplitude characteristic determined according to the specifications for the FIR digital filter to be designed; and

a fourth step of using the transition area ratio determined in the second step, the start point and the end point of the transition area determined in the third step, and the standard function input in the first step to determine an interpolation function of a finite length which joins the start point and end point of the transition area together and which has a period shorter than the standard function by an amount corresponding to the transition area ratio.

43. A computer readable medium containing computer code thereon which, when executed by a computer, carries out functions that generate a numerical sequence for a desired frequency characteristic according to the method steps of claim 33.

34. A device that generates a numerical sequence indicative of a frequency characteristic corresponding to specifications for an FIR digital filter to be designed, the device comprising;

input means for inputting a standard function such that an impulse response from the standard function has a finite value other than zero only in a given area and a value of zero in all the other areas; and

calculation means for performing;

a first operation of determining a transition area ratio that is a ratio of a transition area indicative of an area of a predetermined part between a pass band and a stop band of a frequency amplitude characteristic determined by the standard function input in the first step, to the entire area indicative of an area from the pass band to the stop band,

a second operation of determining an interpolation function length indicative of the length of an effective area in a direction of a frequency axis of the frequency amplitude characteristic of an interpolation function to be determined, from the transition area ratio and the transition area width based on specifications for the FIR digital filter to be designed,

a third operation of using the interpolation function length and the standard function to determine the interpolation function of a finite length which joins a maximum amplitude value at a predetermined frequency position of the frequency amplitude characteristic and a minimum amplitude value at a frequency position that is at a distance equal to the interpolation length from the predetermined frequency position together, the interpolation function having a period shorter than the standard function by an amount corresponding to the interpolation function length, and

a fourth operation of shifting the frequency amplitude characteristic of the interpolation function by a desired amount in the direction of the frequency axis to determine a numerical sequence for a frequency amplitude characteristic corresponding to the specifications for the FIR digital filter to be designed.

37. A computer readable medium containing computer code thereon which, when executed by a computer, carries out functions associated with said calculation means for performing recited in claim 34.

35. A device that generates a numerical sequence indicative of a frequency characteristic corresponding to specifications for an FIR digital filter to be designed, the device comprising;

input means for inputting a standard function such that an impulse response from the standard function has a finite value other than zero only in a given area and a value of zero in all the other areas; and

calculation means for performing a first operation of determining a transition area ratio that is a ratio of a transition area indicative of that area of a frequency amplitude characteristic determined according to the specifications for the FIR digital filter to be designed which contains amplitude values except a maximum amplitude value and a minimum amplitude value, to a transition area indicative of that area of a frequency amplitude characteristic determined by the standard function which contains amplitude values except a maximum amplitude value and a minimum amplitude value, a second operation of using the transition area ratio to determine a start point and an end point of the transition area of the frequency amplitude characteristic determined according to the specifications for the FIR digital filter to be designed, a third operation of using the transition area ratio, the start point and end point of the transition area, and the standard function to determine an interpolation function of a finite length which joins the start point and end point of the transition area together and which has a period shorter than the standard function by an amount corresponding to the transition area ratio.

44. A computer readable medium containing computer code thereon which, when executed by a computer, carries out functions associated with said calculation means for performing recited in claim 35.