JP2003168958A - Digital filter, method, apparatus and program for designing the same - Google Patents

Abstract

<P>PROBLEM TO BE SOLVED: To easily design a digital filter having a desired frequency characteristic. <P>SOLUTION: A waveform of the desired frequency characteristic is inputted as a numeral sequence and the numeral sequence is subjected to inverse FFT (FAST Fourier transformation) to determine a group of filter coefficients. In this way, only by inputting an image of the waveform of the desired frequency characteristic, an FIR (finite impulse resonance) filter having an arbitrary frequency characteristic can be easily designed without any expert knowledge. Also, by performing special rounding arithmetic for the numeral sequence determined by the inverse FFT, the value of filter coefficient is simplified without causing degradation in accuracy of the filter characteristic, and the number of adders used in a filter constituent can be significantly reduced. Further, by performing window arithmetic for the result of the inverse FFT, the length of a numeral sequence inputted at first is made long to suppress a frequency error to be small, the number of filter coefficients is suppressed to be small, and the constitution of a digital filter to be designed can be simplified. <P>COPYRIGHT: (C)2003,JPO

Description

Detailed Description of the Invention

[0001]

BACKGROUND OF THE INVENTION 1. Field of the Invention The present invention relates to a digital filter designing method and designing device, a digital filter designing program, and a digital filter, and more particularly to a tapped delay line including a plurality of delay devices, and a signal of each tap. The present invention relates to a method of designing an FIR filter that is multiplied by several and then added and output.

[0002]

2. Description of the Related Art In various electronic devices provided in various fields such as communication, measurement, voice / image signal processing, medical care, seismology, etc., it is common to perform some kind of digital signal processing internally. Is. The most important basic operation of digital signal processing is a filtering process for extracting only a signal in a required frequency band from an input signal in which various signals and noise are mixed. For this reason, digital filters are often used in electronic devices that perform digital signal processing.

As a digital filter, IIR (Infi
Nite Impulse Response: An infinite length impulse response) filter and FIR (Finite Impulse Response) filter are often used. FI of these
The R filter has the following advantages. First, FIR
The circuit is always stable because the poles of the filter transfer function are only at the origin of the z-plane. Secondly, a perfectly accurate linear phase characteristic can be realized.

When the filters are classified according to the arrangement of the pass band and the stop band, they are mainly low pass filters, high pass filters,
There are four types of filters, a bandpass filter and a band elimination filter. The IIR filter is basically a low-pass filter, and the other high-pass filters, band-pass filters, and band-elimination filters are derived from the low-pass filter by performing processing such as frequency conversion. Also in the FIR filter, the high pass filter and the like are derived from the low pass filter.

For example, when designing a high-pass filter, first, a basic low-pass filter is designed, and the frequency of the low-pass filter is converted. Furthermore, a low-pass filter is designed and frequency conversion is repeated as necessary to design a high-pass filter having a desired frequency characteristic.
In the frequency conversion processing here, based on the ratio between the sampling frequency and the cutoff frequency, the transfer function of the filter is obtained by performing a convolution operation using a window function or Chebyshev approximation method, and further The process of replacing with frequency components is performed.

[0006]

However, the conventional filter design method described above has a problem that it requires a high degree of specialized knowledge such as frequency conversion and thus cannot easily design a filter. Also, although it is possible to manage a typical filter such as a high-pass filter, a band-pass filter, and a band-elimination filter, it is extremely difficult to design a filter having an analog complex waveform as a frequency characteristic. . Further, the frequency conversion using the window function or the Chebyshev approximation method is extremely complicated in its calculation. Therefore, if this is implemented by software, the processing load becomes heavy, and if implemented by hardware, the circuit scale becomes large.

The present invention has been made to solve such a problem, and has an FI having an arbitrary frequency characteristic.
It is an object of the present invention to make it possible to easily design an R digital filter. Further, the present invention is capable of realizing a desired frequency characteristic with high accuracy with a small circuit scale.
It is also intended to be able to easily design the R digital filter.

[0008]

In order to solve the above problems, in the present invention, a numerical sequence or function representing a desired frequency characteristic is input, and the input numerical sequence or function is subjected to inverse Fourier transform to Extracting the resulting real number terms, rearranging the first half and second half of the extracted number sequence consisting of real number terms, and multiplying the number sequence consisting of the above real number terms by 2 ⁿ (n is a natural number) Then, after rounding the number below the decimal point, the result is multiplied by 1/2 ^n, and the numerical value sequence thus obtained is determined as a filter coefficient group.

According to another aspect of the present invention, a numerical sequence or function representing a desired frequency characteristic is inputted, and a numerical sequence or function having more data points than the number of taps of a digital filter is inputted, and the inputted numerical sequence is inputted. Alternatively, the inverse Fourier transform of the function is performed to extract the resulting real number term, and the numerical sequence consisting of the extracted real number terms is rearranged into the first half and the second half, and the numeric sequence consisting of the real number terms. Is multiplied by a predetermined window function, and the numerical sequence obtained thereby is determined as a filter coefficient group.

[0010]

BEST MODE FOR CARRYING OUT THE INVENTION An embodiment of the present invention will be described below with reference to the drawings. FIG. 1 is a flowchart showing the processing procedure of the digital filter designing method according to the present embodiment. The digital filter designed here is a type of FIR filter that includes a delay line with taps composed of a plurality of delay devices, and multiplies the signal of each tap by a given filter coefficient group and then adds and outputs the result. .

In the FIR filter, the impulse response represented by a finite time length is used as the filter coefficient as it is. Therefore, designing the FIR filter means determining the filter coefficient group so as to obtain a desired frequency characteristic. Therefore, the flowchart of FIG. 1 shows a method of determining a filter coefficient group in such an FIR filter.

As shown in FIG. 1, first, a numerical sequence representing a waveform having a desired frequency characteristic is input (step S1). It is preferable that the numerical sequence input at this time has as many data as possible. Originally, in order to form an ideal filter, an infinite number of filter coefficients are required and the number of taps of the filter must be infinite. Therefore,
In order to reduce the error with the desired frequency characteristic, it is preferable to increase the number of input data corresponding to the number of filter coefficients to such an extent that the frequency error falls within a required range.
At least input the numerical value sequence so that the number of data is larger than the number of filter coefficients to be obtained (the number of taps of the digital filter).

For this data input, individual numerical values may be directly input, or a waveform having a desired frequency characteristic may be drawn on the two-dimensional input coordinates for expressing the frequency-gain characteristic, and the drawn waveform may be used. You may make it substitute-input in the numerical value sequence corresponding to it. By using the latter input method, it is possible to input data while confirming the desired frequency characteristic as an image, and thus it is possible to intuitively input data representing the desired frequency characteristic.

There are several possible means for realizing the latter input method. For example, a two-dimensional plane showing frequency-gain characteristics is displayed on a display screen of a computer, and a waveform of a desired frequency characteristic is displayed on the two-dimensional plane by GUI (Gr
A method of drawing with aphical User Interface) and converting it into numerical data is considered. A pointing device such as a digitizer or a plotter may be used instead of the GUI on the computer screen. The method described here is merely an example, and the numerical sequence may be input by a method other than this. Although the desired frequency characteristic is input as a numerical value sequence here, it may be input as a function representing the waveform of the frequency characteristic.

Next, an inverse Fourier transform (inverse FFT) is performed by using the frequency characteristic thus input as a transfer function, and the real number term of the result is extracted (step S2). As is well known, when a Fourier transform (FFT) process is performed on a certain numerical value sequence, a waveform having a frequency-gain characteristic corresponding to the numerical value sequence is obtained. Therefore, if a numerical sequence or a function representing a desired frequency-gain characteristic waveform is input, it is subjected to inverse FFT, and its real term is extracted, the original numerical sequence required to realize the frequency-gain characteristic is obtained. Is obtained.
This numerical sequence corresponds to the filter coefficient group to be obtained.

However, the numerical sequence itself obtained by the inverse FFT is not arranged in the order that it can be used as it is as a filter coefficient group. That is, in any type of digital filter, the numerical sequence of filter coefficients has a symmetric property that the median value is the largest and the value gradually decreases while repeating the amplitude as the distance from the center increases.
On the other hand, the numerical sequence obtained by the inverse FFT has the smallest median value and the largest values at both ends.
Therefore, by rearranging the first half and the second half so that the median value of the numerical sequence obtained by the inverse FFT is at both ends, the median value becomes the maximum value and the front-rear symmetry is obtained (step S3).

Although it is possible to determine the numerical value sequence thus obtained as the filter coefficient group as it is, in the present embodiment, the windowing operation is further performed (step S4). As described above, in the data input stage of step S1, the number of input data is increased to such an extent that the error with the desired frequency characteristic falls within the required range. This number of input data corresponds to the number of filter coefficients.
Therefore, if the numerical sequence obtained by processing such as inverse FFT from this input data is used as it is as the filter coefficient group, the number of taps of the digital filter becomes very large and the circuit scale becomes large. Therefore,
The number of taps is reduced to the required number by performing windowing calculation.

The window functions used at this time include various functions such as a rectangular window, a Hamming window, a Hanning window, and a Hartlet window. Although any window function may be applied, it is particularly preferable to use the Hanning window. This is because the Hanning window has a value of 0 at both ends of the window and is a function in which the value gradually decreases from the central value toward both ends. For example, when a rectangular window is used, the number of taps is forcibly cut off to a finite number, but this causes ringing (waviness) on the filter characteristic. On the other hand, if the filter coefficient is not cut off with a finite value but is gradually changed to 0, the occurrence of ringing can be suppressed.

It is also possible to directly use the numerical value sequence thus obtained as a filter coefficient group. However, the filter coefficient group obtained by the inverse FFT and the windowing operation has a very large number of digits below the decimal point and is a complex and random set of values. Therefore, if this numerical value sequence is used as it is as a filter coefficient group, the number of multipliers required for the digital filter becomes huge, which is not realistic.

Therefore, it is necessary to round off the filter coefficient by rounding down the decimal places of the numerical value sequence. However, in the rounding process by simple truncation, the resulting numerical sequence is still a complicated and random value with only a reduced number of digits, and again requires a large number of multipliers. In addition, if it is simply rounded down, the accuracy of the obtained filter coefficient group is poor and the error with the desired frequency characteristic becomes large. Therefore, in the present embodiment, the rounding operation processing as described below is performed (step S5). That is, the numerical sequence after being windowed in step S4 is multiplied by 2 ⁿ (n is a natural number) to round (decimalize) the decimal point, and the result is multiplied by 1/2 ⁿ .

According to such a rounding operation, all filter coefficients have a value that is an integral multiple of 1/2 ⁿ . Therefore, it is possible to configure the digital filter such that the signal from each tap of the digital filter is individually multiplied by an integral multiple part, all the multiplication outputs are added, and then the product is multiplied by ½ ^n. Becomes Moreover, the integral multiple part can be expressed by addition of binary numbers such as 2 ⁱ +2 ^j + ... (i and j are arbitrary integers). As a result, the number of multipliers used in the entire digital filter can be greatly reduced, and the configuration can be simplified. Also, since the numerical sequence obtained by the inverse FFT is rounded after being multiplied by 2 ⁿ ,
The rounding error can be reduced as compared with the case where the number of digits after the decimal point of the numerical value sequence is simply rounded. As a result, the filter coefficient group can be simplified without degrading the accuracy of the filter characteristics.

In the present embodiment, the numerical sequence obtained by such rounding operation is finally determined as the filter coefficient group. Note that the processes of steps S3 to S5 described above do not necessarily have to be performed in this order, and at least rounding calculation may be performed after the windowing calculation. For example, the windowing calculation may be performed before the rearrangement. In this case, the Hanning window is multiplied so that the coefficient values at both ends of the window are "1" and the coefficient value at the center of the window is "0". By thus performing the windowing calculation at an early stage in the series of procedures, the number of data used for the subsequent calculations can be reduced, and the processing load on the calculations can be reduced.

The procedure of the filter designing method according to the present embodiment described above will be described in detail below with reference to a concrete example. As shown in FIG. 2, in step S1, the frequency-gain characteristic of the filter standardized by "1" is drawn and converted into numerical data. The input data should be symmetrical about the center of the sampling frequency. At this time, the input data length (the length of the graph, that is, the number of numerical sequences) m is a value within the range in which the frequency error is required, and is 2 ^k for simplifying the inverse FFT processing in step S2. To be

For example, the sampling frequency is 44.1K.
When designing an FIR filter for a voice signal of Hz, the relationship between the input data length m and the maximum frequency error is as shown in Table 1 below. The maximum frequency error referred to here corresponds to the frequency per scale of the graph, and 44.
It is obtained by a calculation of 1 KHz / m. In the case of voice processing, if it is about 10 Hz, it falls within the allowable error range, so 4096 is used as the input data length m.

[0025]

[Table 1]

In the example of the graph shown in FIG. 2, the sampling frequency is 44.1 KHz, the input data length m is 4096,
The frequency characteristics correspond to a low-pass filter having a cutoff frequency of 8 KHz and a gain drop amount of -60 dB at the cutoff frequency. In this case, the horizontal axis of the graph is equally divided into 4096 scales (clocks). When the number of clocks is CK, the frequency f at the number of clocks CK is f = CK × (44.1 / 4096) (KHz). Therefore, the clock number C corresponding to 8 KHz
K1 becomes CK1 = f × (4096 / 44.1K) ≈743.04.

In step S2, the frequency characteristic of the low-pass filter input as shown in FIG.
The T process is executed and the resulting real number term is extracted. Further, in the next step S3, in order to convert the numerical sequence obtained by the inverse FFT into an order that can be used as a filter coefficient group, the numerical sequence is divided into the first half and the second half as shown in FIG. Rearrange. That is, the value at the 0th clock is changed to the value at the 2048th clock (hereinafter, 0 → 2048
1 → 2049, 2 → 2050, ...
2047 → 4095, 2048 → 0, 2049 → 1, ...
-Sort as 4095-> 2047.

Furthermore, in step S4, a windowing operation is performed to reduce the number of taps. As described above, the window function includes a rectangular window, a Hamming window, a Hanning window, a Hartlet window, and the like, but here, a Hanning window whose both ends smoothly converge to 0 is used. Here, the relationship between the number of taps limited by the width of the window function and the cutoff characteristic is shown in FIG. As can be seen, the larger the number of taps, the steeper the slope of the characteristic at the cutoff frequency.

Here, an example in which the width of the window function is set so that the number of taps of the digital filter becomes 127 will be shown.
FIG. 5 is a diagram showing the function value of the Hanning window in this case. Hanning window (127 data strings) shown in FIG. 5
Is multiplied by the central part of the numerical value sequence (4096 data sequences) obtained by the rearrangement. At this time, all coefficients outside the Hanning window range are calculated as 0. Then, in the final step S5, the numerical value sequence after the windowing operation is set to 2
^{It is} multiplied by ⁿ and rounded below the decimal point, and the result is multiplied by 1/2 ⁿ (for example, 2 ⁿ = 2048).

FIG. 6 shows a filter coefficient group (127 filter coefficients) obtained by the above calculation. Figure 7
FIG. 7 is a diagram showing a frequency-gain characteristic and a frequency-phase characteristic as a result of FFT of a numerical sequence of filter coefficient groups obtained as shown in FIG. 6, and the frequency-gain characteristic shows the gain on a logarithmic scale. . FIG. 8 is a diagram showing the gain on a linear scale for the same frequency-gain characteristic, and FIG. 9 is a z plan view. As can be seen from FIGS. 7 to 9, the filter coefficient group obtained by the filter design method of the present embodiment has a cutoff frequency of 8 KHz.
The low pass filter characteristic of is realized almost accurately. Moreover, the deduction amount at the cutoff frequency is 40 dB or more, and the phase characteristics are linear and stable.

FIG. 10 is a diagram showing a configuration example of a low-pass filter constructed by using the filter coefficient group obtained by the filter designing method of this embodiment. In this filter, 127 D-type flip-flops 1 connected in cascade
_The input signal is sequentially delayed by 1 clock CK by _-1 to _1-127 . Then, each D-type flip-flop 1 _-1 to 1
_For the signal extracted from the _-127 output taps, the integer value of the result obtained by multiplying the filter coefficient by 2048 is multiplied by 127 coefficient units 2 _-1 to 2 _-127 , respectively, and all the multiplication results are added by 127. The output is made by adding with the units 3 _{-1 to} 3 _-127 .

Then, in the multiplier 4 provided in the output stage of the final stage adder _3-127 , the addition output is divided by 1/2048.
The amplitude is multiplied and returned to the original value, and the result is temporarily held in the D-type flip-flop 5 and then output. Although 127 coefficient units and 127 adders are provided here, the coefficient unit and the adder can be omitted for the portion where the filter coefficient value is zero. Therefore, in reality, it is possible to configure the digital filter with a smaller number of multipliers and adders than in FIG. in this way,
In the present embodiment, a special rounding operation is performed when obtaining the filter coefficient, so that the configuration of the designed digital filter can be simplified.

Although an example of designing a low-pass filter has been described above, other digital filters can be designed similarly. For example, an example of setting a bandpass filter will be described below. Here, as a frequency characteristic of a desired bandpass filter, as shown in FIG.
It is assumed that a numerical value sequence of frequency characteristics as shown in is input. The desired frequency characteristic shown in FIG. 11 is such that only signals in the frequency band of 5 to 8 KHz are passed. Here, again, the sampling frequency is 44.1 KHz and the input data length is 4096.

For the input data shown in FIG. 11, in the same manner as the low pass filter described above, inverse FFT → rearrangement → windowing operation (the window is a Hanning window and the width is 127) →
When the rounding operation is performed, a filter coefficient group as shown in FIG. 12 is obtained.

FIG. 13 is a diagram showing frequency-gain characteristics and frequency-phase characteristics as a result of FFT of the numerical sequence of the filter coefficient group obtained as shown in FIG.
The gain characteristic shows the gain on a logarithmic scale. 14
[Fig. 15] is a diagram showing the gains on a linear scale for the same frequency-gain characteristics, and Fig. 15 is a z plan view. As can be seen from FIGS. 13 to 15, the filter coefficient group obtained by the filter designing method of the present embodiment almost accurately realizes the bandpass filter characteristic of the pass frequency band of 5 to 8 KHz. Moreover, the deduction amount at the cutoff frequency is 40 dB or more, and the phase characteristics are linear and stable.

FIG. 16 is a diagram showing data input as desired frequency characteristics of a low-pass filter for sound quality adjustment used in hearing aids and various audio equipment. The frequency characteristic of the sound quality adjusting low-pass filter is continuously changed in an analog manner. Similarly, inverse FFT → rearrangement → windowing operation → rounding operation is performed on the input data shown in FIG. 16 and the filter coefficient group obtained by this is FFTed to obtain a frequency characteristic as shown in FIG. To be As can be seen from the above, the filter coefficient group obtained by the filter design method of the present embodiment almost accurately realizes the desired frequency characteristic of the low-pass filter for sound quality adjustment. Further, although not particularly shown in the figure, the phase characteristic is linear and stable.

FIG. 18 is a diagram showing data input as desired frequency characteristics of a high-pass filter for sound quality adjustment used in a hearing aid or various audio devices. The frequency characteristics of the high-pass filter for adjusting the sound quality are continuously changed in an analog manner. Similarly, for the input data shown in FIG. 18, inverse FFT → rearrangement → windowing operation → rounding operation is performed, and the filter coefficient group obtained by this is FFTed to obtain a frequency characteristic as shown in FIG. To be As can be seen from the figure, the filter coefficient group obtained by the filter designing method of the present embodiment almost accurately realizes the desired frequency characteristic of the high-pass filter for sound quality adjustment. Further, although not particularly shown in the figure, the phase characteristic is linear and stable.

The apparatus for realizing the digital filter designing method according to the present embodiment described above can be realized by any of hardware configuration, DSP, and software. For example, when it is realized by software, the filter designing apparatus of this embodiment is actually a CPU of a computer or MPU, RAM, RO.
This can be realized by operating a program that is configured by M or the like and is stored in RAM, ROM, hard disk, or the like.

Therefore, it can be realized by recording a program that causes a computer to operate to perform the functions of the above-described embodiment in a recording medium such as a CD-ROM and reading the program by the computer. A recording medium for recording the above program is a CD-RO.
Besides M, a flexible disk, a hard disk, a magnetic tape, an optical disk, a magneto-optical disk, a DVD, a non-volatile memory card or the like can be used. It can also be realized by downloading the above program to a computer via a network such as the Internet.

Further, not only the functions of the above-described embodiments are realized by the computer executing the supplied program, but also the OS (operating system) or other application software running the program on the computer. In the case where the functions of the above-described embodiments are realized in cooperation with the above, or all or part of the processing of the supplied program is performed by the function expansion board or function expansion unit of the computer, the functions of the above-described embodiments are realized However, such a program is also included in the embodiment of the present invention.

As described above in detail, in the present embodiment, the numerical value sequence representing the waveform of the desired frequency characteristic is input as an image, and the filter coefficient group is obtained by performing an inverse Fourier transform on this image. It is possible to easily determine the coefficient of the FIR digital filter that realizes a desired frequency characteristic without requiring a great knowledge of mathematics or electrical engineering. Furthermore, it should be noted that not only low-pass filters, but also high-pass filters, band-pass filters, band-emission filters, comb filters, and analog arbitrary waveform filters can be easily designed using the same method. .

Further, in this embodiment, by performing a special rounding operation on the numerical sequence obtained by the inverse Fourier transform, the filter coefficient group can be simplified without lowering the accuracy of the filter, The number of component multipliers (dividers) used can be significantly reduced. Furthermore, in the present embodiment, since the result of the inverse Fourier transform is multiplied by the window function of the required length, the input data length is lengthened to suppress the frequency error at the same time, and at the same time,
The number of filter coefficients (the number of taps of the digital filter) can be reduced. As a result, the configuration of the designed digital filter can be simplified and desired frequency characteristics can be realized with high accuracy.

It should be noted that the above-described embodiments are merely examples of the implementation of the present invention, and the technical scope of the present invention should not be limitedly interpreted thereby. is there. That is, the present invention can be implemented in various forms without departing from the spirit or the main features thereof.

[0044]

As described above, according to the present invention, a waveform of a desired frequency characteristic is inputted as a numerical sequence or a function, and an inverse Fourier transform is performed to obtain a filter coefficient group. An FIR digital filter having an arbitrary frequency characteristic such as a low-pass filter, a high-pass filter, a band-pass filter, and a band-emission filter can be easily designed without any knowledge.

Further, according to the present invention, the special rounding operation is performed on the numerical sequence obtained by the inverse Fourier transform, so that the accuracy of the filter characteristic is not lowered.
The required filter coefficient group can be simplified, and the number of multipliers used as filter components can be greatly reduced. As a result, it is possible to easily design an FIR digital filter that can achieve desired frequency characteristics with high accuracy on a small circuit scale.

Further, according to the present invention, since the windowing operation is performed on the result of the inverse Fourier transform, the numerical sequence to be input first is lengthened to suppress the frequency error and at the same time the filter coefficient The number (the number of taps of the digital filter) can be reduced, and the configuration of the designed digital filter can be simplified. As a result, it is possible to easily design an FIR digital filter that can achieve desired frequency characteristics with high accuracy on a small circuit scale.

[Brief description of drawings]

FIG. 1 is a flowchart showing a processing procedure of a digital filter designing method according to the present embodiment.

FIG. 2 is a diagram showing an example of a desired frequency characteristic input in step S1 of FIG.

FIG. 3 is a diagram for explaining a rearrangement process in step S3 of FIG.

FIG. 4 is a diagram showing the relationship between the number of taps limited by the width of the window function used in step S4 of FIG. 1 and the cutoff characteristic.

5 is a diagram showing function values of a Hanning window used in step S4 of FIG.

FIG. 6 is a diagram showing a filter coefficient group obtained by applying the filter designing method of the present embodiment from the numerical sequence of the desired frequency characteristic shown in FIG.

7 is a diagram showing a frequency-gain characteristic (logarithmic scale) and a frequency-phase characteristic as a result of FFT of the numerical sequence of the filter coefficient group shown in FIG. 6 obtained by the filter designing method of the present embodiment.

FIG. 8 is a diagram showing frequency-gain characteristics (linear scale) as a result of FFT of the numerical value sequence of the filter coefficient group shown in FIG. 6 obtained by the filter designing method of the present embodiment.

FIG. 9 is a diagram showing az plane as a result of FFT of a numerical value sequence of the filter coefficient group shown in FIG. 6 obtained by the filter designing method of the present embodiment.

FIG. 10 is a diagram showing a configuration example of a digital FIR filter configured by using a filter coefficient group obtained by the filter design method of the present embodiment.

FIG. 11 is a diagram showing another example of the desired frequency characteristic input in step S1 of FIG.

12 is a diagram showing a filter coefficient group obtained by applying the filter designing method of the present embodiment from the numerical sequence of the desired frequency characteristic shown in FIG.

FIG. 13 is a diagram showing a frequency-gain characteristic (logarithmic scale) and a frequency-phase characteristic as a result of FFT of the numerical sequence of the filter coefficient group shown in FIG. 12 obtained by the filter designing method of the present embodiment.

FIG. 14 is a diagram showing a frequency-gain characteristic (linear scale) as a result of FFT of the numerical value sequence of the filter coefficient group shown in FIG. 12 obtained by the filter designing method of the present embodiment.

FIG. 15 is a diagram showing az plane as a result of FFT of the numerical value sequence of the filter coefficient group shown in FIG. 12 obtained by the filter designing method of the present embodiment.

16 is a diagram showing another example of the desired frequency characteristic input in step S1 of FIG.

17 is a diagram showing a frequency characteristic as a result of FFT of a filter coefficient group obtained by applying the filter designing method of the present embodiment from the numerical sequence of the desired frequency characteristic shown in FIG.

18 is a diagram showing another example of a desired frequency characteristic input in step S1 of FIG.

19 is a diagram showing a frequency characteristic as a result of FFT of a filter coefficient group obtained by applying the filter designing method of the present embodiment from the numerical sequence of the desired frequency characteristic shown in FIG.

[Explanation of symbols]

1 _-1 to _1-127 D-type flip-flop 2 _-1 to _2-127 coefficient unit 3 _-1 to _3-127 adder 4 1/2048 times multiplier 5 D-type flip-flop

Claims (9)

[Claims] 1. A method of designing a digital filter, wherein a signal of each tap in a delay line with a tap composed of a plurality of delay devices is multiplied several times by a given filter coefficient group, and then added and output. Enter a numerical sequence or function that represents the frequency characteristics,
The input number sequence or function is inverse-Fourier-transformed to extract the resulting real number term, and the process of rearranging the first half and the second half of the number sequence consisting of the extracted real number term, and the real number A numerical sequence consisting of terms is multiplied by 2 ⁿ (n is a natural number), the number after the decimal point is rounded, and the result is multiplied by 1/2 ⁿ , and the resulting numerical sequence is determined as the filter coefficient group. A method for designing a digital filter, characterized in that 2. A method of designing a digital filter, wherein a signal of each tap in a delay line with a tap composed of a plurality of delay devices is multiplied by a given filter coefficient group and then added and output. A numerical sequence or function representing frequency characteristics,
Input a numerical sequence or function that has more data points than the number of taps of the digital filter, extract the real number term of the result by performing an inverse Fourier transform of the input numerical sequence or function, and make up the extracted real number term. For the numerical sequence, the process of rearranging the first half and the latter half, and the process of multiplying the numerical sequence consisting of the real number term by a predetermined window function, the numerical sequence obtained by this is the filter coefficient group A method for designing a digital filter, characterized in that 3. A numerical sequence before or after the numerical sequence consisting of real terms as a result of the inverse Fourier transform is rearranged, or the numerical sequence after being multiplied by the window function is multiplied by 2 ^n. 3. The method of designing a digital filter according to claim 2, wherein (n is a natural number), the number after the decimal point is rounded, and the result is multiplied by 1/2 ⁿ . 4. A digital filter design apparatus for multiplying the signals of each tap in a delay line with taps composed of a plurality of delay devices by a given filter coefficient group, and then adding the signals to obtain a desired signal. An input means for inputting a numerical sequence or a function representing the waveform of the frequency characteristic, an inverse Fourier transform means for performing an inverse Fourier transform on the numerical sequence or the function inputted by the input means, and extracting a real number term of the result; A rearranging means for rearranging the first half and the second half of the numerical sequence obtained by the Fourier transform, and the numerical sequence of the real number terms before or after being rearranged by the rearranging means are multiplied by 2 ⁿ ( (n is a natural number), rounds the number after the decimal point, and rounds the result by 1/2 ^n. In the digital filter design apparatus, the numerical sequence rounded by the rounding means is determined as the filter coefficient group. 5. A device for designing a digital filter, which multiplies the signals of each tap in a delay line with taps composed of a plurality of delay devices by a given filter coefficient group, and then adds and outputs the signals. A numerical sequence or function representing the waveform of the frequency characteristic, the input means for inputting a numerical sequence or function having more data points than the number of taps of the digital filter, and the numerical sequence or function input by the input means. Inverse Fourier transform, and an inverse Fourier transform means for extracting the resulting real number term, rearrangement means for rearranging the first half and the second half of the numerical sequence obtained by the inverse Fourier transform, and the rearrangement means for arranging And a window processing means for multiplying the numerical sequence before or after being rearranged by a predetermined window function, the rearranging means Together are more sorting, the design device of the digital filter, characterized in that the sequence of numerical values are windowed by the windowing means is adapted to determine as the filter coefficient group. 6. A numerical sequence before or after being rearranged by said rearranging means or a numerical sequence after being windowed by said window processing means is multiplied by 2 ⁿ (n is a natural number). And round the number after the decimal point to 1 /
The apparatus for designing a digital filter according to claim 5, further comprising rounding means for performing a process of multiplying by 2 ⁿ . 7. The means for drawing the waveform of the desired frequency characteristic on a two-dimensional input coordinate for expressing the frequency-gain characteristic, and the drawn waveform as the numerical sequence or function. 7. A device for designing a digital filter according to claim 4, further comprising means for inputting. 8. A digital filter design program for causing a computer to function as each unit according to any one of claims 4 to 7. 9. A digital filter designed by using the designing method according to any one of claims 1 to 3 or the designing apparatus according to any one of claims 4 to 7.