How to Design a lowpass filter by cascading 10 sections of the first-order IIR lowpass filter

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HADIMARGO 2020-12-1

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此问题的直接链接

https://ww2.mathworks.cn/matlabcentral/answers/671928-how-to-design-a-lowpass-filter-by-cascading-10-sections-of-the-first-order-iir-lowpass-filter

评论： HADIMARGO 2020-12-2

采纳的回答： Mathieu NOE

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I design all of this filter but i can't understand how to make filter cascading 10 section.

out teacher said you can conv the transfer function 10 time but it didn't work. any idea?

%% low-pass IIR cascade K = 10 and compare with first-order low pass 
clc; clear all; close all;
w = 0:pi/255:pi;
% For Tenth-Order Low-Pass IIR | Transfer Function
num1 = [1 1];
den1 = [1 0.31];
y = (num1) / (den1) ;
for i=1:9
    y = conv (y,y)
end
h1 = freqz(y, 1, w);
g1 = 20*log10(abs(h1));
% PLOT CODE For Tenth-Order
figure (2);
plot(w/pi,g1);grid minor; axis ([0 1 -100 5]);
xlabel("\omega /\pi");ylabel("Gain in dB");
title("LOW-PASS Cascade K=10 IIR Filter");

i had problem in conv part that its result is incorrect.

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Answer 1

Mathieu NOE 2020-12-2

1
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https://ww2.mathworks.cn/matlabcentral/answers/671928-how-to-design-a-lowpass-filter-by-cascading-10-sections-of-the-first-order-iir-lowpass-filter#answer_563168

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hello

yes , conv is doing what your professor is asking , but this is the right way to use it (on the num and den part of your IIR filter)

%% low-pass IIR cascade K = 10 and compare with first-order low pass 
clc; clear all; close all;
w = 0:pi/255:pi;
% For Tenth-Order Low-Pass IIR | Transfer Function
num1 = [1 1]/1.5267;  % the /1.5267 is to make static gain = 1 (0 dB) (my suggestion)
den1 = [1 0.31];
% y = (num1) / (den1) ;
num = num1; % init
den = den1; % init
h1 = freqz(num, den, w);
g1 = 20*log10(abs(h1));
% PLOT CODE For first-Order
figure (1);
plot(w/pi,g1);grid minor; axis ([0 1 -100 5]);
xlabel("\omega /\pi");ylabel("Gain in dB");
title("LOW-PASS Cascade K=1 IIR Filter");
for i=1:9
    num = conv (num,num1);
    den = conv (den,den1);
end
h1 = freqz(num, den, w);
g1 = 20*log10(abs(h1));
% PLOT CODE For Tenth-Order
figure (2);
plot(w/pi,g1);grid minor; axis ([0 1 -100 5]);
xlabel("\omega /\pi");ylabel("Gain in dB");
title("LOW-PASS Cascade K=10 IIR Filter");