JPH0223050B2 - - Google Patents

Description

DETAILED DESCRIPTION OF THE INVENTION The present invention relates to a digital filter that can approximate arbitrary frequency (amplitude) characteristics on a non-linear frequency scale.

Conventionally, methods for approximating the frequency characteristics of a digital filter to desired characteristics include a design method using a linear phase finite impulse response filter, Johnson's method, and the like.

However, the digital filters obtained by these methods all approximate the frequency characteristics on a linear frequency scale.

Incidentally, recently, digital filters have been used to synthesize voices and musical instrument sounds, but in order to obtain high-quality synthesized sounds during such synthesis, it is necessary to use MEL, which is suitable for the characteristics of human hearing. ) It is desirable to use a scale that can closely approximate the desired spectrum on a non-linear frequency scale.

This invention was made in view of the above circumstances,
It is an object of the present invention to provide a digital filter that can approximate desired frequency (amplitude) characteristics on a non-linear frequency scale such as the Mel scale.

An embodiment of the present invention will be described below with reference to the drawings.

First, a method of approximating characteristics on a nonlinear frequency scale will be described. The transfer function H(z) of the digital filter that we are trying to realize now is a polynomial of the transfer function H _A (z) of a suitable all-range filter, H(Z)=Ho(ω)= _M 〓 ^m=0 g _n ω ^m ...(1) ω=H _A (z) ...(2) It is assumed that it is given as follows.

The frequency characteristic of this all-pass filter H _A (e ^j 〓) [where Ω=ω△t, ω is the angular frequency, and △t is the unit delay time of the digital filter] is H _A (e ^j 〓) = e ^{- j} 〓 ……(3) Ω^＝α(Ω)＝−argH _A (e ^j 〓) ……(4).

Therefore, the desired frequency characteristic H of the filter is
(e ^j 〓) is H (e ^j 〓) = H _O (H _A (e ^j 〓)) = H _O (e ^-j 〓) = _M 〓 ^m=0 g _n e ^-jm 〓 ……(5) becomes.

Also, the coefficient g _n of the polynomial H _O (ω) is the desired frequency (amplitude) characteristic G given at the nonlinear frequency Ω^
Choose one that can approximate (Ω^) with the value of equation (5).

The digital filter obtained at this time is constructed as shown in FIG. That is, in FIG. 1, H _A (z) is an all-pass filter, g _n is a coefficient circuit, and AD is an adder circuit.

Now, the transfer function H _A (z) as an all-pass filter is H _A (z)=z ^-1 -a/1-az ^-1 (a=0.375)...(6
), H _A (z)=e ^-j 〓−a/1−ae ^-j 〓=cosΩ−j si
nΩ-a/1-a cosΩ+ja sinΩ = (cosΩ-a) (1-a cosΩ)-a sin ² Ω
-j[cosΩ(cosΩ-a)+sin(1-a cosΩ)]/
(1-a cosΩ) ² +a ² sin ² Ω...(7) However, the argument angle in the above equation is Ω^=tan ^-1 a sinΩ(cosΩ-a)+sinΩ(1-
a cosΩ)/(cosΩ-a) (1-a cosΩ)-a s
in ² Ω＝tan ^-1 (1−a ² )sinΩ／(1+a ² )cosΩ−2a…
...(8), which can be well approximated to the Mel scale as the phase characteristic of the filter.

Incidentally, when formula (8) is illustrated, it is shown as a solid line in Figure 2, which closely approximates the Mel scale shown as a broken line.

By the way, the desired amplitude characteristic G on the Mel frequency scale
(Ω^) Fourier coefficient g _n = 1/2π∫〓 _- 〓G(Ω^)e ^jm 〓dΩ^ ...(9) According to, the transfer function H(z) of the filter becomes H(Z)= Ho(ω)= _2M 〓 ^m=0 g _nM ω ^m ……(10) ω=H _A (z) ……(11) It is assumed that it is given by.

The frequency characteristic H (e ^j 〓) of this filter is H (e ^j 〓) = _2M 〓 ^m=0 g _nM (H _A (e ^j 〓)) ^m = _2M 〓 ^m=0 g _nM e ^-jm 〓 =e ^-jM 〓 _M 〓 ^m=-M g _n e ^-jm 〓 ……(12). Here, _M 〓 ^m=-M is g _n e ^-j 〓 is the M-order partial sum of the Fourier series of G (Ω^), and even if the value takes a negative value in a specific interval, it is a negative interval. is small and has a small value, so the amplitude characteristic |H(e ^j 〓)| is extremely close to the one that best approximates G(Ω^) in the sense of minimizing the root mean square error.

Therefore, the amplitude characteristic G on the Mel frequency scale
The transfer function H(z) is (9)(10)(11) as a filter that best approximates (Ω^) in the sense of minimizing the root mean square error.
You can consider what is given by the formula.

In this way, the desired frequency characteristics can be approximated on a non-linear frequency scale such as the Mel scale, so when synthesizing voices, musical instruments, etc., high-quality synthesis that matches the characteristics of human hearing can be achieved. You can get the sound.

[Brief explanation of drawings]

FIG. 1 is a schematic configuration diagram showing an embodiment of the present invention, and FIG. 2 is a characteristic diagram for explaining the embodiment. H _A (z)...All-pass filter, g _n ...Coefficient circuit,
A _D …Addition circuit.

Claims (1)

[Claims] 1. Replace the plurality of delay elements of the non-recursive filter with the same all-pass filter, and set the Fourier coefficient g _n = 1/2π of the desired amplitude characteristic G (Ω^) on the Mel frequency scale. ∫〓 _- 〓G(Ω^)e ^jm 〓dΩ^, the filter transmission relation H(z) is H(Z)=Ho(ω)= _2M 〓 ^m=0 g _nM ω ^m ω=H _A ( z), and is characterized in that it is possible to approximate arbitrary frequency (amplitude) characteristics on a non-linear frequency scale.