JPH0770955B2 - Filter coefficient calculation setting method - Google Patents

Description

BACKGROUND OF THE INVENTION 1. Field of the Invention The present invention relates to a method for calculating and setting a filter coefficient of an equalizer using a transversal filter.

2. Description of the Related Art In recent years, with the digitization of audio equipment, development of a device using a transversal filter (hereinafter referred to as FIR filter) capable of realizing an arbitrary frequency characteristic has been advanced.

FIG. 3 shows a conventional filter coefficient calculation device for calculating the filter coefficient required to obtain a desired frequency characteristic by the FIR filter. In FIG. 3, when an arbitrary amplitude frequency characteristic | H (ω) | is input from the input unit 1 for each sampling frequency of the first type (or the second type), it is input in the first computing unit 2. From amplitude frequency characteristics | H (ω) |
The transfer function is obtained from the linear phase condition by using the sampling frequency of the seed (or the second kind), and the inverse Fourier transform unit 3 performs the first transfer function.
The filter coefficient is obtained by inverse Fourier transform from the transfer function obtained by the calculation unit 2 of. In the second calculation unit 4, the filter coefficient obtained in the inverse Fourier transform unit 3 is windowed, and in the setting circuit 5, the windowed filter coefficient is calculated in the second calculation unit 4.
It is configured to set the FIR filter 6.

The desired amplitude frequency characteristic | H (ω) | is determined by the input unit 1 as the first type sampling frequency ω = (2 · π / N) · k (however, k
= 0 to N−1, N: number of sampling points). When the second type of sampling is performed, ω = (2 · π / N) (k + 1 /
2) Input every time. An example of the amplitude frequency characteristics input at the sampling frequency of the first type is shown in FIG. 4 (a), and FIG. 4 (b).
Shows an example of the amplitude frequency characteristic input at the second type sampling frequency. In FIG. 4, the number of sampling points is N = 2
The sampling points are indicated by 0 and black circles.

Next, the transfer function H (ω) is calculated by the following equation from the linear phase condition in the first calculation unit 2.

If H (ω) = H _R (ω) + jH _I (ω)… (1), then H (ω) = | H (ω) | ・ e ^−jaω … (2) From H _R (ω) = | H (ω) | ・ cos (αω) (3) H _I (ω) =-| H (ω) | ・ sin (αω) (4) However, since it is a linear phase, α = (N-1 ) / 2, N: number of sampling points (5).

When the first type of sampling was performed, ω = (2 · π / N) · k (6) k = 0 to (N−1), and the second type of sampling was performed. In this case, ω = (2 · π / N) (k + 1/2) (7) k = 0 to (N−1).

FIG. 5 (a) shows sampling frequency points of the first kind taken on the unit circle of the Z plane, and FIG. 5 (b) shows sampling frequency points of the second kind. In FIG. 5, the number of sampling points is N = 8, and black circles indicate sampling points.

If the amplitude frequency characteristic | H (ω) | is given as described above, the transfer function at each frequency point can be obtained from the third and fourth equations.

It should be noted here (of course) that the amplitude frequency characteristic is obtained by the first type sampling (that is, the frequency point is obtained as in the sixth equation, and the amplitude frequency characteristic is obtained at that point. Is sampled), ω in the third and fourth equations is obtained by the sixth equation, that is, (K = 0 to N−1, N: number of sampling points).

Further, when the sampling of the amplitude frequency characteristic is performed by the second type sampling, ω must be calculated using the seventh expression.

Next, the transfer function H (ω) thus obtained in the inverse Fourier transform unit 3 is subjected to inverse Fourier transform to obtain the filter coefficient (impulse response to H (ω)). (At this time, the impulse response becomes a real number, but usually an imaginary part occurs as an error in actual calculation. However, this is ignored and only the real part is taken out for calculation.) The inverse Fourier transform is It is executed by an expression.

ω = (2π / N) · k or ω = (2π / N) (k + 1/2) 0 ≦ n ≦ N−1 Here, it should be noted that the sampling of the first kind was performed. In this case, naturally, ω must use the sixth equation, and if the second type sampling is performed, the seventh equation must be used. However, when the second type of sampling is performed, the relationship as in the following equation may be used.

The h (n) obtained as described above is multiplied by an appropriate window function W (n) (Hanning, Hamming window, etc.) in the second computing unit 4 as shown in the twelfth equation, and the FIR is actually calculated.
The filter coefficient set in the filter 6 is obtained.

h ′ (n) = h (n) · W (n) (12) When W (n) is Hanning, it is expressed by the following equation.

W (n) = 1 / 2.multidot. [1-cos (2.pi.n / (N-1))] (0.ltoreq.n.ltoreq.N-1) (13) h '(n) obtained by the 12th equation is As the filter coefficient, the setting circuit 5 sets the FIR frequency in the FIR filter 6, and the amplitude frequency characteristic given here is realized.

FIG. 6 shows a flow chart of a filter coefficient calculation algorithm in the above-described conventional filter coefficient calculation device.

Problems to be Solved by the Invention In such a conventional configuration, the window function W (n) is multiplied to the impulse response h (n) after the inverse Fourier transform as shown in the twelfth formula. This is because the ideal impulse response that realizes the given amplitude frequency characteristics has an infinite length, while the actual calculation result using Eq. 10 has a finite length, so the impulse response obtained by Eq. 10 If is used as it is as a filter coefficient, a ripple is usually generated on the amplitude frequency characteristic. A window function is applied to prevent this.

In this way, in the past, since the impulse response after the inverse Fourier transform cannot be used as it is as a filter coefficient, it is necessary to use this impulse response multiplied by some window function. It has the drawback of long quantity and long calculation time.

SUMMARY OF THE INVENTION It is an object of the present invention to provide a method for calculating and setting a filter coefficient that can accurately realize a desired amplitude frequency characteristic without ripples without actually multiplying it by a window function.

Means for Solving the Problems A method for calculating and setting a filter coefficient according to the present invention uses a sampling frequency ω1 of a first type or a sampling frequency ω of a second type shown below.
2, an amplitude frequency characteristic is input, a transfer function is obtained from the input amplitude frequency characteristic, and when the amplitude frequency characteristic is set at the first type sampling frequency, the second type sampling frequency characteristic Inverse Fourier transform of the transfer function to obtain an impulse response, and when the sampling frequency of the second type is set, the impulse response is obtained by performing an inverse Fourier transform of the transfer function with the sampling frequency characteristic of the first type. Is obtained, and the real part of the impulse response obtained by the inverse Fourier transform is set as an external transversal filter as a filter coefficient.

ω1 = (2 ・ π / N) ・ k ω2 = (2 ・ π / N) ・ k (+1/2) However, k = 0 to N-1 operation According to this configuration, the input amplitude frequency characteristic is The transfer function is used as it is (that is, the imaginary part is zero), and when the amplitude frequency characteristic is input at the sampling frequency of the first type, the inverse Fourier transform is performed at the sampling frequency of the second type to make an impulse response. When the amplitude characteristic is input at the second sampling frequency, the inverse Fourier transform is performed by the sampling frequency of the first type to calculate the impulse response, and the real part of the obtained impulse response is used as a filter coefficient. Since it is set to an external transversal filter, desired amplitude frequency characteristics can be accurately realized without ripples without using a window function.

Embodiment Hereinafter, a method for calculating and setting a filter coefficient of the present invention will be specifically described with reference to FIGS. 1 and 2.

FIG. 1 shows a block diagram of a filter coefficient calculation device adopting the calculation setting method of the present invention. In FIG. 1, when an arbitrary amplitude frequency characteristic is input from the input circuit 7 for each sampling frequency of the second type, the inverse Fourier transform circuit 8 uses the input amplitude frequency characteristic as a transfer function to perform sampling of the first type. Inverse Fourier transform by frequency. In the setting circuit 9, the real part of the impulse response obtained by the inverse Fourier transform circuit 8 is set in the FIR filter 6 as a filter coefficient.

In the input circuit 7, desired amplitude frequency characteristic | H
(Ω) | is set for each sampling frequency of the second type (see FIG. 4B), and this amplitude frequency characteristic is transferred to the transfer function H.
Let (ω).

_{That, H (ω) = H R} (ω) + jH I (ω) ... (14) H R (ω) = | H (ω) | ... and _{(15) H I (ω)} = 0 ... (16) .

In this way, the obtained transfer function H (ω) has a linear phase. This can be understood from the following equation.

H (ω) = | H (ω) | = e ^jaω・ | H (ω) | ・ e ^−jaω … (17) From the property of Fourier transform, h (n + m) e ^jmω・ H '(ω)… (18) The impulse response obtained by using the amplitude frequency characteristic as it is as the transfer function H (ω) from the equations 17 and 18 is the equation 3 and the equation 4
It can be seen that the impulse response obtained from the transfer function obtained from the equation is delayed by m, and the equation shows that the transfer function H (ω) has a linear phase. From this transfer function H (ω), the inverse Fourier transform circuit 8 performs an inverse Fourier transform of the following equation 19 using the first type sampling frequency to obtain an impulse response to H (ω).

(0 ≦ n ≦ N−1, H (ω) is a value obtained by the 14th equation, the 15th equation, and the 16th equation.) Here again, the complex function e in the 17th equation
The ω of ^jωn is a value when the first type of sampling represented by the sixth equation is performed, and is not the second type sampling frequency of the seventh equation.

Here, when the sampling frequency of the second type is used, ripples occur in the amplitude frequency characteristic that is realized without applying a window.

Next, the setting circuit 9 extracts the real part of the impulse response h (n) obtained by the inverse Fourier transform circuit 8 and sets this value in the FIR filter 6 as a filter coefficient. The characteristics can be accurately realized without causing ripples.

FIG. 2 shows a flowchart of the filter coefficient calculation algorithm of the above filter coefficient calculation device.

Although the case where the amplitude frequency characteristic is input at the second type sampling frequency has been described so far, when the amplitude frequency characteristic is input at the first type sampling frequency, the above calculation is performed. The same effect can be obtained by performing the calculation by reversing the sampling frequencies of the first and second types.

EFFECTS OF THE INVENTION As described above, according to the present invention, the input amplitude frequency characteristic is used as the transfer function, and the transfer function is subjected to the second sampling when the amplitude frequency characteristic is input at the first sampling frequency. In frequency, when the amplitude frequency characteristic is input at the second sampling frequency, an inverse Fourier transform is performed at the first sampling frequency to obtain an impulse response, and the real part of the obtained impulse response is used as a filter coefficient for external Since it is set in the FIR filter, the desired amplitude frequency characteristic can be accurately realized without ripple even without using the window function used to prevent the ripple that occurs in the amplitude frequency characteristic that is actually realized. Therefore, the amount of calculation and the calculation time can be reduced as compared with the conventional case because the window function is not used.

[Brief description of drawings]

1 and 2 show a specific example of the calculation setting method of the present invention, FIG. 1 is a block diagram of a transversal filter coefficient calculation device, and FIG. 2 is a flowchart showing a filter coefficient calculation algorithm. FIG. 4 is a block diagram of a conventional filter coefficient computing device, FIG. 4 is an amplitude frequency characteristic diagram showing an example of sampling points of amplitude frequency characteristics, FIG. 5 is an explanatory diagram of an example of sampling frequency points, and FIG. It is a flowchart figure which shows the filter coefficient calculation algorithm in a prior art example. 6 ... FIR filter, 7 ... input circuit, 8 ... inverse Fourier transform circuit, 9 ... setting circuit.

 ─────────────────────────────────────────────────── ─── Continuation of the front page (56) Reference JP 63-246914 (JP, A) JP 63-26112 (JP, A) JP 63-93211 (JP, A) JP 63- 244924 (JP, A) JP 63-234617 (JP, A) JP 63-278410 (JP, A) JP 6-91416 (JP, B2) US Patent 4896285 (US, A) European patent application Publication 284175 (EP, A)

Claims (1)

[Claims] 1. An amplitude frequency characteristic is input by a first type sampling frequency ω1 or a second type sampling frequency ω2 shown below, a transfer function is obtained from the input amplitude frequency characteristic, and the amplitude frequency characteristic is obtained. When the sampling frequency of the first type is set, the transfer function is inverse-Fourier-transformed by the sampling frequency characteristic of the second type to obtain an impulse response, and the sampling frequency of the second type is set. In this case, the transfer function is inverse-Fourier-transformed with the sampling frequency characteristic of the first type to obtain an impulse response, and the real part of the impulse response obtained by the inverse-Fourier transformation is set as a filter coefficient in an external transversal filter. How to set the calculation of the filter coefficient. ω1 = (2 · π / N) · k ω2 = (2 · π / N) · (k + 1/2) where k = 0 to N−1