JPS63244924A - Filter coefficient arithmetic unit - Google Patents

Abstract

PURPOSE:To control the frequency characteristics of amplitude and a phase independently, by setting impulse response for the characteristics of the amplitude and the phase on a transversal filter (FIR) as filter coefficients. CONSTITUTION:At an amplitude input circuit 5, a desired amplitude frequency characteristic ¦H(omega)¦ wherer it is omega=0-pi is set, and to a correction characteristic input circuit 6, the reverse amplitude frequency characteristic ¦H1(omega)¦ of the one on which phase correction is desired to be applied is inputted. A phase frequency characteristic, that is, the reverse phase characteristic of the one on which the phase correction is desired to be applied is found by performing Hilbert transformation at an arithmetic circuit 7, and the impulse response h(n) is found at a reverse Fourier transformation circuit 8 by applying reverse Fourier transformation from the amplitude frequency characteristic and the phase frequency characteristic. Since the frequency characteristics of the amplitude and the phase of the impulse response are set as the filter coefficients on the FIR, it is possible to control the frequency characteristics of the amplitude and the phase independently.

Description

DETAILED DESCRIPTION OF THE INVENTION Field of the Invention The present invention relates to a filter coefficient calculation device for an equalizer using a transversal filter (hereinafter referred to as an FIR filter) that realizes arbitrary amplitude frequency characteristics and phase frequency characteristics. It is something.

Conventional technology In recent years, along with the digitization of audio equipment? , there is a demand for the development of an equalizer using an FIR filter.

However, in conventional equalizers, it has not been possible to independently control the amplitude frequency characteristics and the phase frequency characteristics using one FIR filter.

FIG. 6 shows a block diagram of a conventional filter coefficient calculating device for calculating filter coefficients of an FIR filter that can control only amplitude frequency characteristics.

In Fig. 6, 1 is an arbitrary amplitude frequency characteristic I H (→
1 is an input circuit that inputs the input signal; 2 is an inverse Fourier transform circuit that uses the input amplitude frequency characteristic as a transfer function and performs inverse Fourier transform on this transfer function to obtain filter coefficients;
3 is a setting circuit that sets the determined filter coefficients in the FIR filter, and 4 is an FIR filter that realizes the actually given amplitude frequency characteristics.

The desired amplitude frequency characteristic IH (→1 is inputted by the input unit 1. An example of the input amplitude frequency characteristic is shown in FIG. 6. In FIG. 6, N: the number of sampling points is 20.
The black circle indicates the input point (however, ω−
The characteristics of π-2π are created by folding the input characteristics of ω=〇-π).

Next, in the inverse Fourier transform unit 2, the transfer function H (→=l
H(4)1 ・・・・・・・・・・・・・・・
As (1), the filter coefficient (impulse response to H(→)) can be obtained by performing inverse 7-lier transform on H(ω).

The inverse Fourier transform is performed as shown in the following equation.

h(→=1/N・ΣH(→・e rise 0 ・・・・・・・・・
・・・・・・・・・(2) 2π・K (ω”y O≦n≦N−1) h (n is set in the FIR filter 4 by the setting circuit 3 as a filter coefficient , the amplitude frequency characteristic given here will be realized.The phase frequency characteristic becomes a linear phase by giving the transfer function by equation (1).

Problems to be Solved by the Invention However, in the conventional example shown in FIG. 6, although any amplitude frequency characteristic can be achieved as mentioned at the beginning, the phase frequency characteristic is uniquely determined by the number of tap coefficients of the FIR filter. The disadvantage is that the linear phase is fixed and the phase frequency characteristics cannot be set arbitrarily.

In view of the above-mentioned problems, the present invention provides a filter coefficient calculation device that independently sets arbitrary amplitude frequency characteristics and arbitrary phase frequency characteristics and obtains filter coefficients of an FIR filter that can realize them.

Means for Solving the Problems In order to solve the above problems, the present invention provides amplitude input means for inputting amplitude frequency characteristics, phase input means for inputting phase frequency characteristics, and input amplitude frequency characteristics and phase input means. It is comprised of an inverse Fourier transform means that obtains filter coefficients by performing an inverse 7-lier transform on a transfer function having frequency characteristics, and a setting means that sets the filter coefficients in an external FIR filter.

Function: According to the present invention, a desired amplitude frequency characteristic 1 phase frequency characteristic is inputted by the amplitude input means and the phase input means, and the impulse response is obtained by the inverse Fourier transform means which inverse Fourier transforms the transfer function having the amplitude frequency characteristic and the phase frequency characteristic. is calculated, and the impulse response determined by the setting means is set in an external FIR filter as a filter coefficient, thereby realizing desired characteristics.

EXAMPLE Hereinafter, a first example of the present invention will be described with reference to the drawings. FIG. 2 shows a block diagram of a filter coefficient calculation device in an embodiment of the present invention.

In Fig. 2, 6 is an amplitude input circuit for inputting a desired amplitude frequency characteristic, and 6 is an amplitude input circuit for inputting the inverse amplitude frequency characteristic of the amplitude frequency characteristic of the thing for which phase correction is to be performed, such as the inverse amplitude frequency characteristic of a speaker (or phase correction A correction characteristic input circuit (which inputs the amplitude frequency characteristic of the input circuit and automatically creates its inverse characteristic) calculates the phase frequency characteristic from the Hilbert transform relationship from the amplitude frequency characteristic input in the correction characteristic input circuit 6. 8 is an inverse Fourier transform circuit that performs inverse Fourier transform of a transfer function having the amplitude frequency characteristic inputted by the amplitude input circuit 6 and the phase frequency characteristic obtained by the phase calculation circuit 7; 9 is an inverse Fourier transform circuit 8; A setting circuit that sets the impulse response found in
It is an IR filter.

The operation of this embodiment will be described below with reference to the drawings.

In the amplitude input circuit 6, a desired amplitude frequency characteristic IH (→1) of ω=0−π is set, and by folding back this input amplitude frequency characteristic, an amplitude frequency characteristic of ω−π−2π is automatically created ( (See Figure 6).

Next, input the inverse amplitude frequency characteristic IH1 (→1) of what you want to perform phase correction (for example, correcting the phase frequency characteristic of a speaker, etc.) in the correction amplitude input circuit 6. This amplitude frequency characteristic is also of ω-0-π. Enter the amplitude frequency characteristics,
By folding this input amplitude frequency characteristic, ω−π−
A 2π amplitude frequency characteristic is produced. The arithmetic circuit 7 uses this amplitude frequency characteristic to calculate the phase frequency characteristic from the Hilbert transform relationship.

The method of determining the phase frequency characteristic of something with this amplitude frequency characteristic from the amplitude frequency characteristic using the Hilbert transform relationship is as follows (for example, Reference 1: Digital Signal Processing (Part 2), Translated by Gen Date, Corona Publishing, Reference Reference 2: Fundamentals of Digital Signal Processing (Maeda Watari Ohmsha).

The Hilbert transform is originally a method of calculating a complex function from a given real or imaginary function.

A periodic function h(n) with a period N (hereinafter, the sequence of numbers represents a discrete time sequence) is an even function that is a periodic function. (n) and an odd function h0 (→).

h(n)-h. (→+h0(n) ・
・・・・・・・・・・・・・・・('4(n口o-N-1
) Also, if we define periodic causality as the following equation, h (n)
= O, -N/2 < n < O...
・・・・・・・・・(4h(→=h,(n)・u(n)
・・・・・・・・・・・・・・・(Sometimes, h(=) can be found by h e (n).

Here it is. (If we look at the properties of → and h 0(n),
The following can be seen.

The Fourier series coefficient of h(n) is H(6)-HR(6)+tH(6)...
・・・・・・・・・・・・(6) (ω-go ``K.
-o~N-1), the Fourier series coefficient of he(n) becomes HR(6), and the Fourier series coefficient of ho(→ becomes jH
,(X) K, becomes.

From the above results, if we look at the above sequence as a finite period function of finite period N, it conversely becomes HR(IQ(K-o-N-
1) Inverse Fourier transform (usually called IDFT)
This shows that the result becomes h,(n).

From the above properties, we can understand the following.

A transfer function H'(K) that realizes the desired amplitude frequency characteristic IH-(6)1 is set as shown in the following equation.

H/(埒-l H/(6)1・ej″(→ ・・・・
......Shaving (the phase frequency characteristic is θ(ω)) Taking the natural logarithm of both sides of equation (7), l nH'(lQ=ln IH"(K) l + lθ
(→ ・−・−・・・・−(8).

Here, h
'(b), and the inverse Fourier transform of 1nlH'(Q+ is h',,(n), then (from the four holes h'(b) = h4(→・U(b)...
It can be seen that (9) is obtained.

Furthermore, when h'(ω) found from the equation (@) is Fourier transformed, the real part of the found value is 1nlH'(Q+
Also, the imaginary part corresponds to jθ(ω).

Therefore, to summarize the above, to obtain the phase frequency characteristic from the amplitude frequency characteristic: (1) Take the natural logarithm of the amplitude frequency characteristic.

@) Perform inverse Fourier transform on the value found in (1) above.

(3) Calculate h'(ω) using the formula c4 from the above results.

G4) Perform inverse Fourier transform on h'(ω).

(5) Extract the imaginary part of the inverse 7-lier transform of h'(ω).

You can see that if you do this operation. The phase frequency characteristic determined in this way behaves so that the phase shift is minimized (the phase frequency characteristic of a closed speaker system, etc. exhibits such a characteristic).

From the above, if the amplitude frequency characteristic IH1 (→1 is given),
It can be seen that the phase frequency characteristic of something with this amplitude frequency characteristic can be determined from the Hilbert transform relationship.

Therefore, if a phase frequency characteristic having this amplitude frequency characteristic is determined from the inverse amplitude frequency characteristic of the object to be subjected to phase correction, this becomes the phase frequency characteristic for performing phase correction.

In other words, it is possible to obtain the opposite phase characteristics of the object for which phase correction is desired.

Next, in the inverse Fourier transform circuit 8, a transfer function H(ω) having these frequency characteristics is considered from the amplitude frequency characteristics inputted by the amplitude input circuit 6 and the phase frequency characteristics calculated by the phase calculation circuit 7, and this is The impulse response h(ω) is obtained by performing inverse Fourier transform.

In the impulse response obtained in this manner, the amplitude frequency characteristic indicates the amplitude frequency characteristic inputted by the amplitude input circuit 6, and the phase frequency characteristic indicates the phase frequency characteristic calculated by the phase calculation circuit 7. This can be understood if you think about it as follows.

Consider a system with two FIR filters as shown in FIG. 11 inputs an arbitrary amplitude frequency characteristic, calculates the phase frequency characteristic θ, 1 (ω) from the Hilbert transform relationship from this amplitude frequency characteristic, and filters the transfer function with this frequency characteristic by inverse Fourier transform. FIR filter A, 12 used as a coefficient is the desired amplitude frequency characteristic IH1° (→1 and the amplitude frequency characteristic obtained by adding the inverse amplitude frequency characteristic of the amplitude frequency characteristic inputted in FIR filter A11 (the amplitude frequency characteristic is input in LOG logarithm) FIR coefficient is the value obtained by inverse Fourier transform of the transfer function (the amplitude frequency characteristic itself can be used as the transfer function, that is, the phase term is set to zero) obtained from the linear phase condition. FIR7 (filter B). With this configuration, the amplitude frequency characteristic of the entire system is FIR filter B1.
The amplitude frequency characteristic input in step 2 is IH1゜(ω)1, and the phase amplitude frequency characteristic is θ11 (→(Actually, the change in linear phase of FIR filter B12 is added, but when considering phase correction, the influence of this is (In other words, when considering the phase term, the group delay characteristic obtained by differentiating the phase frequency characteristic with respect to frequency is considered, so the change in the linear phase is ignored.) Therefore, conversely, the overall Looking at the system, a system that has one FIR filter with a phase frequency characteristic determined from the relationship between arbitrary amplitude frequency characteristics and Hilbert transform has one linear phase FIR filter and Hilbert transform (minimum phase transition). It can be seen that this is equivalent to an FIR filter composed of two FIR filters having the following relationship:

In this way, h(fI
) has arbitrary amplitude frequency characteristics and phase frequency characteristics for correction.

Next, in the setting circuit 9, h
(n) is set as a filter coefficient in the FIR filter 10 that realizes the actually input frequency characteristics.

In this embodiment, the phase correction of a certain thing has been explained as an example, but it is also possible to realize the phase frequency characteristic of a thing having a certain amplitude frequency characteristic.

FIG. 1 is a block diagram showing a second embodiment of the invention. 13 is a phase characteristic input circuit into which an arbitrary phase frequency characteristic is input. In FIG. 3, parts having the same functions as those shown in FIG. 2 are designated by the same numbers.

The phase characteristic input circuit 13 receives an arbitrary phase characteristic from ω=0 to π. The characteristic of ω=π−2π is produced by folding the phase characteristics of ω=0−π with different signs. This comes from the condition that when the desired impulse response is a real number, the amplitude frequency characteristic is an even function and the phase frequency characteristic is an odd function.

The operation is similar to that of the first embodiment, the only difference being that the phase frequency characteristic is calculated from the given amplitude frequency characteristic for phase correction or is directly input.

However, in this embodiment, the phase frequency characteristic is not only the minimum phase shift but also any arbitrary phase frequency characteristic. As shown in the first example, the amplitude-frequency characteristic to be realized is obtained by inputting an arbitrary amplitude-frequency characteristic, and the phase-frequency characteristic is obtained from the Hilbert transform relationship, and the filter coefficients are calculated from the inverse Fourier transform. By finding , it was possible to set the phase and amplitude independently. From this,
It can be seen that the phase frequency characteristics can also be set to arbitrary characteristics.

To explain this, consider the part in which the phase frequency characteristic is determined using the Hilbert transform relationship in the first embodiment.

In the first embodiment, the phase frequency characteristic is obtained from the inverse amplitude frequency characteristic of the object for which a certain phase correction is to be performed. Suppose that this is reversed, a certain phase frequency characteristic is set, and an amplitude frequency characteristic corresponding to this is obtained. In other words, when the obtained amplitude frequency characteristic is input, it is considered that the set phase frequency characteristic is obtained from the Hilbert transform relationship.

Therefore, it is considered that an amplitude frequency characteristic exists for any phase frequency characteristic.

This will be explained using FIG. 3 shown above. 11, the FIR filter A112 is set with a filter coefficient corresponding to a transfer function obtained from an amplitude frequency characteristic having an arbitrary set phase frequency characteristic, and the FIR filter A 112 has an arbitrary set amplitude frequency characteristic. The amplitude frequency characteristic is the sum of the amplitude frequency characteristic obtained from the phase frequency characteristic of the FIR filter A11 and the inverse amplitude frequency characteristic, and the FIR filter is set with the filter coefficient obtained from the transfer function obtained from the linear phase condition. Let it be B.

By adopting such a configuration, as in the first embodiment, the overall amplitude frequency characteristic can be changed to any amplitude frequency characteristic 2 phase frequency characteristic set in the FIR filter B12.
The phase frequency characteristic is set by the filter A11.

Considering this, it can be seen that the configuration shown in the second embodiment allows the amplitude frequency characteristic and the phase frequency characteristic to be set independently.

FIG. 4 is a block diagram showing a third embodiment of the present invention. 14 is a group delay input circuit into which an arbitrary group delay characteristic is input; 16 is an integration circuit which calculates a phase frequency characteristic by integrating the group delay characteristic inputted in the group delay input circuit 14. In FIG. 4, parts having the same functions as those shown in FIG. 2 are designated by the same numbers.

The group delay characteristic τ(a/) is as follows: τ(→=dθ(→/dω)
・・・・・・(1o) is defined as Therefore, similarly to the first and second embodiments, the amplitude frequency characteristic and the group delay characteristic (phase frequency characteristic) can be set independently.

In addition, 1. Second. In the third embodiment, the impulse response obtained by the inverse Fourier transform circuit 8 is directly used as the filter coefficient of the FIR filter 1o, but if this is done, ripples may occur on the frequency characteristics realized in the FIR filter 1o. . In order to prevent this, the impulse response determined by the inverse Fourier transform circuit 8 is sometimes multiplied by a window function having certain characteristics (Hanning, Hamming, etc.), and this is used as the coefficient of the FIR filter 1o.

Therefore, it should be added that the setting circuit 9 also includes settings that are made using such a window.

Effects of the Invention The present invention provides amplitude input means for inputting amplitude frequency characteristics;
A phase input means for inputting a phase frequency characteristic, an inverse Fourier transform means for obtaining an impulse response to a transfer function having the input amplitude frequency characteristic and phase frequency characteristic, and an external By providing a setting means for setting the transversal filter, it is possible to provide a filter coefficient calculation device that calculates filter coefficients that can independently control amplitude frequency characteristics and phase frequency characteristics.

[Brief explanation of the drawing]

Figures 1, 2, and 4 are block diagrams of a filter coefficient calculation device according to an embodiment of the present invention, Figure 3 is a block diagram showing the same filter coefficient calculation algorithm, and Figure 6 shows a conventional example. The block diagram and FIG. 6 are characteristic diagrams showing a method of setting amplitude frequency characteristics. 6... Amplitude input circuit, 6... Correction characteristic input circuit, 7... Phase calculation circuit, 8...
・Inverse Fourier transform circuit, 9...Setting circuit, 10
...FIR filter, 1191102. FIR
Filter, 12...FIR filter, 13...
...Phase input circuit, 14...Group delay input circuit. Name of agent: Patent attorney Toshio Nakao and 1 other person No. 1
Figure 2 Figure 3. 5 6 pu

Claims (6)

[Claims] (1) An amplitude input means for inputting an arbitrary amplitude frequency characteristic, a phase input means for inputting an arbitrary phase frequency characteristic, and an inverse Fourier that calculates an impulse response to a transfer function having the input amplitude frequency characteristic and phase frequency characteristic. 1. A filter coefficient calculation device comprising a conversion means and a setting means for setting an impulse response obtained by inverse Fourier transformation as a filter coefficient in an external transversal filter. (2) The phase-amplitude input means includes a corrected amplitude input means for inputting an arbitrary corrected amplitude-frequency characteristic, and an operation for calculating a phase-frequency characteristic from a Hilbert transform relationship based on the corrected amplitude-frequency characteristic input by the corrected amplitude input means. and a filter coefficient is determined by an inverse Fourier transform means from a transfer function having an amplitude frequency characteristic input by the amplitude input means and a phase frequency characteristic determined by the calculation means. The filter coefficient calculation device according to item 1. (3) The phase input means includes a group delay input means for inputting the group delay frequency characteristic τ(ω), and an integrating means for calculating the phase frequency characteristic by integrating the group delay frequency characteristic, and the amplitude input means 2. The filter coefficient calculation device according to claim 1, wherein a filter coefficient is determined by an inverse Fourier transform means from a transfer function having an amplitude frequency characteristic inputted by the integer and a phase frequency characteristic determined by the integrating means. (4) The amplitude input means inputs only the amplitude frequency characteristic in the range of ω = 0 - π (ω: angular frequency), and generates the amplitude frequency characteristic in the range of ω = π - 2π by folding back this amplitude frequency characteristic. 2. The filter coefficient calculation device according to claim 1, wherein this is taken as the overall amplitude frequency characteristic. (5) The phase input means inputs only the phase frequency characteristic in the range of ω = 0 - π (ω: angular frequency), reverses the sign of this phase frequency characteristic, and then folds it back to the range of ω = π - 2π. 2. The filter coefficient calculation device according to claim 1, wherein the filter coefficient calculation device generates a phase frequency characteristic of 1 and uses this as the entire phase frequency characteristic. (6) The apparatus according to claim 1, further comprising a window means for applying a certain window to the impulse response obtained by the inverse Fourier transform means, and the impulse response obtained by applying the window is used as a filter coefficient. Filter coefficient calculation device.