[matlab] IIR filter

One .IIR filter

    IIIR The unit impulse response of the filter is infinite ！ Expressed by difference equation as ：

     It can be seen from the above formula , Calculate the output y(n) When , Previous output and input values are required . In other words ,iirl The filter has a feedback link . When $a_k$ When it's zero , This filter has no feedback , Its unit shock response is limited , yes FIR filter . When $a_k$ Not for 0 It is time to , yes IIR filter .

Two .IIR The structure of the filter

（1） direct I type

     Obtained directly from the difference equation IIR The filter is called direct I Type structure , As shown in the figure below , On the left is the zero point part , On the right is the pole ：

（2） direct II type

     Merging the same delay units is direct II type

3、 ... and . The reference sample

（1） Basic knowledge of

（2） direct I Type example

     Design a filter with order 7, Sampling frequency is 20Mhz, Cut off frequency 5Mhz, The stopband attenuation is 60dB One of the matlab filter ( With cheby2 For example );
Method 1 ： call matlab Built-in function
[b,a]=cheby2(n,$R_p$,$W_n$)
n： The order of the filter
$R_p$： Maximum attenuation of passband ripple
$W_n$： Cut off frequency ,fs Normalize to $2\pi$,$W_n=f_{stop}/fs\ast 2$

clc;
clear all;
fs=2000e4;   
f0=200e4;    
f1=800e4;    
M=1999;
n=0:(M-1);
N=11; % Quantized digits 
% signal = sin(2*pi*f0/fs*n);
signal = sin(2*pi*f0/fs*n)+sin(2*pi*f1/fs*n);
[b,a]=cheby2(7,60,0.5);  % 500/2000*2=0.5
signal_f = filter(b,a,signal);
fft_plot(signal,fs,' Signal before filtering ');
fft_plot(signal_f,fs,' Filtered signal ');
signal=round(signal./max(signal))*(2^N-1);
fid = fopen('sin1.txt','w');
fprintf(fid,'%d\n',signal);  % x representative 16 Base number   d For decimal 
fclose(fid);
fft_plot(signal,fs,' The quantized signal before filtering ');
signal_f = filter(b,a,signal);
fft_plot(signal_f,fs,' Quantized signal after filtering ');
function fft_plot(y,fs,s_name)
    L_i = 2^nextpow2(length(y)*100);
    s_i_fft = fft(y,L_i);
    s_i_fftshfit = fftshift(s_i_fft);
    P = abs(s_i_fftshfit)/length(y)*2;   % For non DC components or 0 It's divided by N multiply 2, For the DC component, it is directly divided by N 
%     fshift = (-L_i/2:L_i/2-1)*(fs/L_i);
    fshift = linspace(-fs/2,fs/2,L_i);
    figure;
    plot(fshift,P);
    title([s_name,' Bilateral spectrum of  ']);
    xlabel('f (Hz)');
    ylabel('|P(f)|');
end

Method 2 ：FDATOOL
The parameters are as follows ：

choice Export


export SOS and G To the workspace , take SOS and G To [b,a], The formula is as follows ：

[b1,a1]=sos2tf(SOS,G);

Usually observe the coefficient and find , The coefficients of the two designs are consistent .
matlab The simulation results are as follows ：

As you can see from the diagram 8Mhz The signal of is filtered .
Method 3 ：verilog The implementation of the 【 Specific references 2】

Simulation results ：

Four . Reference material

1. IIR Filter design （ call MATLAB IIR Function to implement ）
2. FPGA Digital signal processing （ 6、 ... and ） Direct type IIR filter Verilog Design
3. About Matlab of use fdatool Design filters
4. Special topic of digital filter design （ One ）——FDATool Use the tutorial