JPS6348206B2 - - Google Patents

Description

DETAILED DESCRIPTION OF THE INVENTION The present invention relates to a sample-based Nyquist filter that processes a sampled digital signal so that the impulse response crosses zero at a Nyquist interval T _N and operates at a sampling rate T.

A Nyquist filter blocks components above the frequency range, and the impulse response is within the Nyquist interval.
It crosses zero at T _N. When data is passed through this filter at a code rate of 1/T _N =f _N /2, it is possible to identify each code without intersymbol interference, and this filter is widely used for data transmission. When this Nyquist filter is configured as a cyclic type,
In the past, the zero crossing points were shifted due to the quantization of the filter series, so it was necessary to increase the coefficient word length in order to obtain the desired zero crossing impulse response.

The purpose of this invention is to shorten the coefficient word length because the zero crossing point is not affected by coefficient quantization, and to reduce the amount of sample hardware by sharing the cyclic term of each digital filter connected in parallel. The purpose of the present invention is to provide a Nyquist filter based on the Nyquist filter.

When the operational sampling interval of the filter is T (seconds), the Nyquist interval is usually T _N =KT (an integer where K>1). This relationship is shown in FIG. 1st
The figure is an example of a filter's impulse response. The transfer function of the filter with sampling interval T is H(Z)
shall be. Here, Z=e ^J 〓 ^TThis transfer function H(Z) can be expanded as follows.

H(Z)= _k-1 〓 ⁱ⁼⁰ Z ^-i Hi(Z ^K ) (1) Equation (1) shows that the filter with transfer function H(Z) has an operation sampling interval of KT and a transfer function of Z ^-i Hi. (Z ^K )(i
This shows that it can be constructed by connecting K filters in parallel (=0, 1...K-1). Transfer function H
If the impulse response of the filter (Z) completely crosses zero at the Nyquist interval T _N =KT, then the operation sampling interval is KT and the transfer function is Z ^-i Hi
Any one of the K filters of (Z ^K ) is T _N
= The impulse response crosses zero exactly at intervals of KT.

Letting this be Z ^-M H _M (Z ^K ) and Z ^-M H _M (Z ^K )=h ₀ Z ^-N ₀ (2), this transfer function is N ₀ T=(M+nK)T
(n is a positive integer) has a non-zero response of h ₀ only.

For example, when T _N =3T, the transfer function H(Z) is expressed as the sum of three filters with a sampling rate of 3T as follows.

H (Z) = H ₀ (Z ³ ) + Z ^-1 H ₁ (Z ³ ) +Z ^-2 H ₂ (Z ³ ) (3) H ₀ (Z ³ ), Z ^-1 H ₁ (Z ³ ), Z The impulse response of ^-2 H ₂ (Z ³ ) is shown in A, B, and C of FIG. 2, and the impulse response of H (Z) is shown in D of the same figure, respectively. That is H ₀
(Z ³ ) filter T(=
The spectrum becomes h ₀ at N ₀ T), and it becomes exactly zero every 3T=T _N , and the filter of Z ^-1 H ₁ (Z ³ ) corresponds to Z ^-1 as shown in Figure 2B. A time response occurs every 3T from a point shifted by T.
In the filter Z ^-2 H ₂ (Z ³ ), as shown in FIG. 2C, a time response occurs every 3T from a point shifted by 2T corresponding to Z ^-2 . These Figure 2 A, B,
The sum of the time responses of C becomes the filter of H(Z) shown in FIG. 2D, and the impulse response of this filter of H(Z) crosses zero exactly at T _N.

Therefore, in general, to realize a filter with a transfer function H(Z) whose impulse response crosses zero at T _N , the operation sampling interval T _N =
At KT, the transfer function is H ₀ (Z ^K ) ~ _{H M} (Z ^K ) ~ _{H K-1} (Z ^K )
Filters 1 ₁ to 1 _M to 1 _K-1 are provided, and these filters 1 ₀ to 1 _M to 1 _K-1 have delay amounts of 0 to MT to
(K-1)T delay circuits ₂₀ to _2M to _2K-1 are connected in series, respectively. One end of these series connections is connected to an input terminal 11, and the other end is connected to an adder circuit 12, and the output of the adder circuit 12 is supplied to an output terminal 13 as a filter output. Note that since the delay circuit 2 ₀ has a delay amount of zero, the filter 1 ₀ is actually connected directly to the adder circuit 12 . Further, the filter 1 _M is a circuit that realizes Z ^{- M} H _M (Z ^K ) = h ₀ Z ^{- N} ₀ in equation (2).

When the filters 1 ₀ to 1 _K-1 are cyclic filters, the configuration can be simplified by making the cyclic terms of their transfer functions common. That is, the transfer function Hi(Z ^K ) is generally expressed by the following equation.

Hi (Z ^K )=Pi (Z ^K )/Qi (Z ^K ) (4) In equation (4), generally Qi (Z ^K )=Q (Z ^K )i=0,
1..., K-1 (≠M). In this case, let the cyclic term in the denominator of equation (4) be a common cyclic circuit. That is, the fourth
As shown in the figure, a circuit 14 that realizes a transfer function 1/Q (Z ^K ) operating at a sampling rate T _N is connected to the input terminal 11, and the output side thereof has a transfer function
P ₀ (Z ^K ) ~ _{P K-1} (Z ^K ) acyclic filter 3 ₀ ~
3 _K-1 and delay circuits 2 ₀ to 2 _K-1 are connected in series, and the output side of the series connection is connected to the adder circuit 12 . The input terminal 11 is connected to the adder circuit 12 through a series circuit of a filter _1M and a delay circuit _2M .

As mentioned above, the sampling rate of the input signal to the Nyquist filter is Nyquist T _N , and the sampling rate of the filter for each transfer function Hi (Z ^K ) after decomposing the transfer function H (Z) is also Nyquist T Since _N ,
The Hi (Z ^K ) filter can reduce the sampling rate to 1/K compared to the H (Z) filter, and there is no increase in hardware due to decomposition. Further, as shown in FIG. 4, the hardware can be reduced by bringing the cyclic term 1/Q (Z ^K ) to the front and using it in common for all Hi (Z ^K ). For example, consider a case where the order of Hi(Z ^K ) is second order.
The multipliers required to realize Hi(Z ^K ) with a digital filter are three for the numerator Pi(Z ^K ) and two for the denominator 1/Qi(Z ^K ). Therefore, in the configuration of FIG. 3, if blocks of 1 ₀ to 1 _K-1 are configured as Hi(Z ^K ), a total of 5K multipliers are required. On the other hand, by making the denominator 1/Q (Z ^K ) common and placing it in front of the whole as shown in Figure 4, the number of multipliers can be reduced.
It can be reduced to 3K+2. Furthermore, since the Nyquist filter according to the present invention crosses zero exactly at the Nyquist interval, there is no deterioration in the time domain due to coefficient rounding of the filter, and there is an advantage that the coefficient word length can be shortened compared to conventional circuit configurations.

[Brief explanation of the drawing]

Figure 1 shows an example of the impulse response of a Nyquist filter, and Figure 2 shows the sampling rate T _N
FIG. 3 is a block diagram showing an example of the configuration of a sample-based Nyquist filter according to the present invention, and FIG. FIG. 2 is a block diagram showing an example of the configuration of a sample-based Nyquist filter according to the invention. 1 ₀ ~ 1 _K-1 , 3 ₀ ~ 3 _K-1 : Sampling rate
T _N filter, 2 ₀ to 2 _K-1 : delay circuit, 11: input terminal, 13: output terminal, 41: circuit.

Claims (1)

[Claims] 1. In a sample-based Nyquist filter whose impulse response crosses zero at the Nyquist interval T _N and operates at a sampling rate T = T _N /K (K is a positive integer), with T _N as the sampling rate, multiplication is performed. vessel,
a cyclic first filter means comprising an adder and a delay device; and a second delay means including at least one delay device having a sampling rate of T, the first filter means and the second delay means; A sample system Nyquist filter characterized in that at least two third means each having a cascade-connected circuit are connected in parallel, and the output signals of the respective parallel circuits are added to obtain an overall output signal. 2. In a sample-based Nyquist filter whose impulse response crosses zero at the Nyquist interval T _N and operates at a sampling rate T = T _N /K (K is a positive integer), where T _N is the sampling rate, a multiplier,
a first filter means of an acyclic type comprising an adder and a delay device; and a second delay means including at least one delay device having a sampling rate of T, the first filter means and the second delay means having a sampling rate of T. a third means in which the means are connected in cascade; a fourth cyclic filter means having a sampling rate of T _N and comprising a multiplier, an adder, and a delay device; and a delay device having a filter and a sampling rate of T. and a fifth means connected in series, an input signal is input to the fourth means and the fifth means, and the fourth means is connected in series.
A sample system characterized in that the output signal of the means is input to a circuit in which at least two of the third means are connected in parallel, and the output signals of the third means and the fifth means are added to obtain an overall output signal. Nyquist filter.