JPH0119292B2 - - Google Patents

Description

DETAILED DESCRIPTION OF THE INVENTION The present invention relates to a digital filter that can be configured with a low filter order and that removes phase distortion and aliasing distortion when reproducing a signal at a sampling frequency lower than the sampling frequency of a recorded signal. The purpose is to provide a digital filter that can

Generally, the signal shown in Figure 1 recorded on a random access memory (RAM) or tape is processed at a sampling frequency lower than the sampling frequency at the time of recording (1/2 to 1/3 of the time at recording). In the case of reading in terms of degree), it is performed using an infinite impulse response (IIR) digital filter expressed by the difference equation of equation (1) below.

Y _o =a _{0 X o + a 1} X _{o - 1} + _a 2 X _o is the time obtained by sampling the signal X(t) (t indicates time) at intervals of time T
The input digital signal at time nT, Y _o is the output digital signal at time nT, and a ₀ to _{a 2} , b ₁ , and b ₂ are coefficients, respectively.

The IIR digital filter has amplitude characteristics as shown in FIG. 1A. In such an IIR digital filter, when the output signal is thinned out, an output of 1/M times is required when extracting every M sample values (M is an integer).

Therefore, for example, if M is "10", the above IIR
When using a digital filter, a transfer function of "5 (order) x 10 = 50 (order)" is required for both the denominator and the numerator as a transfer function expression representing the IIR digital filter.

On the other hand, when a finite impulse response (IIR) digital filter performs the same operation as the above-mentioned IIR digital filter, a transfer function of about 100th order is required. In this case, the signal performance is about 12 bits and the signal band is about 15kHz, but if these specifications were applied more strictly, the order of the transfer function of the above FIR digital filter would increase significantly, making filter design difficult. , which also affects the occurrence of calculation errors and the size of the device.

Therefore, conventional digital filters have a drawback that they have a large number of orders, which causes many calculation errors and makes it difficult to miniaturize the device.

The present invention eliminates the above-mentioned drawbacks,
An embodiment thereof will be explained with reference to FIG. 2 and the following figures.

FIG. 2 shows a block system diagram of an embodiment of the digital filter according to the present invention. In Figure 2,
An input signal enters the input terminal 2 and is supplied to the low-pass filter 1 . This low-pass filter 1 is a finite impulse response (FIR) digital filter 3.
and an infinite impulse response (IIR) digital filter 4 are connected in series.

The FIR digital filter 3 is normally an acyclic digital filter, and is expressed by the following difference equation (2).

y _o = _N-1 〓 ⁱ⁼⁰ a _i x _oi - (2) In the above formula (2), N is the filter order and a _i is the coefficient. The frequency characteristics of this FIR digital filter 3 are as shown by the _broken line in _{FIG .} It exhibits a low-pass characteristic in which the frequency F' _S at the end of the attenuation range is selected to be slightly higher than the frequency _1/2 .

As the IIR digital filter 4, a digital equalizer previously proposed by the present applicant in Japanese Patent Application No. 55-23672 (Japanese Unexamined Patent Publication No. 56-120211) can be used. In this case, the frequency characteristic of the digital equalizer is the fourth
As shown by the solid line in the figure, the end of the passband is at the frequency F _p
, and exhibits a pass characteristic selected such that the end of the attenuation range is at a frequency F _S slightly lower than the frequency _1/2 (where F _S > F _p >F' _p ). A description of the configuration of the digital equalizer proposed above is omitted in this application.

Generally, the IIR digital filter 4 is a cyclic digital filter, and its difference equation can be expressed by the following equation.

p _o = a ₀ y _o + a ₁ y _o-1 + a ₂ y _o-2 −b ₁ p _o-1 −b ₂ p _o-2 ―(3) In the above equation (3), p _o is at time nT Output digital signal, y _o is input digital signal at time nT,
a ₀ to _{a 2} , b ₁ , and b ₂ are coefficients, respectively.

In this embodiment, the transfer function H(z ^-1 ) of the IIR digital filter 4 in the z-domain is determined from equation (3) as follows.

H (z ^-1 ) = a ₀ 1 + a ₁ z ^-1 + a ₂ z ^-2 /1 + b ₁ z ^-1 +b ₂ z ^-2
-(4) Here, as shown in Figure 5, the input signal is
When converting to a signal sampled at a sampling frequency of ₁ , if _S is a digital filter expressed by the transfer function of equation (4), then the relationship between ₁ and _S is expressed by equation (5) below.

_S = 2k ₁ (k is an integer) - (5) If "z ^-1 " in equation (4) above is replaced with "z ^-k ", H(z ^-k ) = a ₀ 1 + a ₁ z ^-k + a ₂ z ^-2k /1+b ₁ z ^-k +b ₂ z ^-2
k ―(6). As can be seen from equation (6), the IIR digital filter 4 uses z ^-k as a unit delay element and has a two-type, two-zero configuration. Next, if we rewrite the above equation (4) in the form of a difference equation, we get p _o = a ₀ y _o + a ₁ y _ok + a ₂ y _o-2k −b ₁ y _ok −b ₂ y _o-2k ―(7) Become.

The IIR digital filter 4 expressed by the above equation (7) has an apparent filter order of "2", but because of the relationship shown in equation (5), in reality, equation (7) is doubled. Therefore, the filter order of the IIR digital filter 4 is substantially "4".

Furthermore, as shown in the equation (7), the digital filter 1 expressed by the above equation ( ₇₎ uses the input and output for every _K pieces as sample values. For example, when the value of M in the variable speed playback device shown in FIG. 3 is "10", the order of the denominator and numerator is "2 x 5 (order) = 10 (order)". However, the frequency characteristics of IIR digital filter 4 are
As shown by a in FIG. 5, since there is folding, it is necessary to remove this unnecessary folded frequency component using the FIR digital filter 3 in advance.
To do this, it is generally sufficient to prepare an FIR digital filter with a filter order of about 20th order, so the filter order of the FIR digital filter 3 is 20/10 (order/M) = 2 (order )”.
Therefore, the filter order of digital filter 1 is
Since the filter orders of FIR digital filter 3 and IIR digital filter 4 are calculated together, "2
(Next) + 4 (Next) = 6 (Next)”.

The filter order of the digital filter 1 is reduced to about 1/10 when compared with the filter order of the conventional example, so as is clear from the above examples, the larger the value of M, the more the present invention The rate of decrease in the filter order of the digital filter increases.

By the way, if the relationship between _S and ₁ is not an even relationship as shown in equation (5), the filter order of the digital filter can be determined as 2 _S = 2k ₁ - (8) or _S = 3k ₁ - (9) using the above method. You can ask for it. In the case of the relationship shown in equation (9) above, when the value of M in Figure 3 is "10", the order of the denominator and numerator above is "3 x 5 (order) = 15
(next)'' However, when combined with the FIR digital filter 3 as described above, the filter order of the digital filter 1 becomes 6th.

In addition, if you want to make the phase characteristic of the IIR digital filter 4 linear, as shown in _FIG .
By using a design method such as removing resonance characteristics with FIR, the overall passband can be made to have a linear phase.

FIR digital filter 3 obtained as described above
The overall frequency characteristic of the digital filter 1 consisting of the IIR digital filter 4 and IIR digital filter 4 is as shown by the solid line in FIG.

Also, FIR and IIR digital filters 3 and 4
Two or more of these may be connected in series to obtain the same characteristics as above.

As described above, the digital filter according to the present invention includes at least one finite impulse response digital filter in which the unit delay time (sampling time) supplied with the input signal is one delay unit, and the output signal of the finite impulse response digital filter. The finite impulse response digital filter is connected in series with at least one infinite impulse response digital filter as an input signal, and the finite impulse response digital filter has an amplitude characteristic that cancels out a peak near the roll-off frequency in the amplitude characteristic of the following infinite impulse response digital filter. , the infinite impulse response digital filter has a delay time that is an integer multiple of the sampling time and a delay time that is twice this delay time as unit delay times, and these are divided into two poles.
Since it is configured with a zero point and has a linear phase characteristic in the passband, the order of the digital filter is lower than that of conventional filters, making it easier to design the filter, and the unit delay element of the infinite impulse response digital filter Since is z ^-k , z ^-1
The number of calculation circuits can be reduced to 1/k compared to the case of It has features such as being able to remove phase distortion and aliasing distortion when reproducing signals.

[Brief explanation of drawings]

Fig. 1 is a spectrum diagram of a variable digital filter, Fig. 2 is a block system diagram showing an embodiment of the digital filter according to the present invention, Fig. 3 is a block system diagram of a variable speed reproducing device, and Fig. 4 is a block system diagram showing an embodiment of the digital filter according to the present invention.
A frequency characteristic diagram showing the frequency characteristics of the FIR digital filter and digital equalizer, Figure 5 is a frequency characteristic diagram of the IIR digital filter, and Figures 6 A and B are respectively
Frequency characteristic and phase characteristic diagram of IIR digital filter. FIG. 7 is a comprehensive frequency characteristic diagram of the digital filter. 1...Digital filter, 2...Input signal, 3...
FIR digital filter, 4...IIR digital filter, 5...output signal, 6...input signal, 7...low-pass digital filter, 8...filter output signal, 9...decimator.

Claims (1)

[Claims] 1 At least one finite impulse response digital filter whose input signal is supplied with a unit delay time (sampling time) as one delay unit, and at least one infinite impulse response whose input signal is an output signal of the finite impulse response digital filter. consisting of a series connection with a digital filter, the finite impulse response digital filter having a frequency Fp' at the end of the passband lower than a frequency _1/2 corresponding to half the sampling frequency ₁ ;
The infinite impulse response digital filter has a low-pass characteristic in which the frequency at the end of the attenuation range is selected to be slightly higher than the frequency _1/2 .
A delay time that is an integer multiple of the sampling time and a delay time that is twice this delay time are each defined as a unit delay time, and furthermore, if the frequency Fp at the end of the passband is lower than the frequency _1/2 and the end of the attenuation region The frequency Fs is the frequency ₁ /
A digital filter characterized in that it has a pass characteristic selected to be slightly lower than 2 (Fs>Fp>Fp').