How to design a low pass filter with rectangular window?

Question

Kalasagarreddi Kottakota 2023-7-7

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此问题的直接链接

https://ww2.mathworks.cn/matlabcentral/answers/1992873-how-to-design-a-low-pass-filter-with-rectangular-window

评论： Kalasagarreddi Kottakota 2023-7-7

Hello all, Here, I have a lowpass filter with butter 15Hz cutoff freqeuncy. But I am looking for a low pass filter using rectangular window implimentation.

clear all;

% close all; clc;

%-------------------------------------------------------------

% System definition %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%

%-------------------------------------------------------------

fs=8192; % sampling frequency

dt = 1/fs; % sample time

T=3; % duration of the signal

Nt = T*fs; % total number of samples

t = 0:dt:T-dt; % time vector

% Source definition

f0 = 900; % initial angular speed in Hz

fT = 2700; % final angular speed in Hz

finst = linspace(f0,fT,Nt);

phi = 2*pi*cumsum(finst)*dt;

a1 = 45;

b1 = 5000;

c1 = 2;

c2 = 1.5;

d1 = 2+3*1j;

% Definition of envelop

int_phi0 = 3*pi/4;

A = d1+(a1 * exp(-b1 * (t - T/c1).^2 + 1j * int_phi0));

% Definition of source signal

q = A.'.*exp(1j*phi).';

filtorder =6; fc =15;%----------------------------------% fc-cutoff

[bcoeff,acoeff] = butter(filtorder,fc/fs*2);

Afilt = filtfilt(bcoeff,acoeff,q.*exp(-1j*phi).');

figure()

plot(t,q,'k')

Warning: Imaginary parts of complex X and/or Y arguments ignored.

hold on

plot(t,abs(Afilt),'r','LineWidth',2)

grid on; box on;

legend('q(t)','A(t)')

xlabel('s')

ylabel('Amp')

title('q(t) and A(t) - filtered')

set(gca,'FontSize',15)

xlim([1.2 1.8])

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Answer 1

N A POORNA CHANDRA 2023-7-7

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此回答的直接链接

https://ww2.mathworks.cn/matlabcentral/answers/1992873-how-to-design-a-low-pass-filter-with-rectangular-window#answer_1268753

在 MATLAB Online 中打开

hi kalasagarreddi, here is the code for low pass filter with rectangular window

clear all;
clc;
fs = 8192;               % Sampling frequency
dt = 1/fs;               % Sample time
T = 3;                   % Duration of the signal
Nt = T*fs;               % Total number of samples
t = 0:dt:T-dt;           % Time vector
f0 = 900;                % Initial angular speed in Hz
fT = 2700;               % Final angular speed in Hz
finst = linspace(f0,fT,Nt);
phi = 2*pi*cumsum(finst)*dt;
a1 = 45;
b1 = 5000;
c1 = 2;
c2 = 1.5;
d1 = 2+3*1j;
%envelop
int_phi0 = 3*pi/4;
A = d1 + (a1 * exp(-b1 * (t - T/c1).^2 + 1j * int_phi0));
% source signal
q = A.'.*exp(1j*phi).';
% Low-pass filter using Kaiser window
fc = 15;                               % Cutoff frequency in Hz
normalized_fc = fc / (fs/2);           % Normalized cutoff frequency
filter_order = 50;                     % Filter order
beta = kaiser(filter_order+1, 8);      % Kaiser window with beta = 8
h = fir1(filter_order, normalized_fc, 'low', beta); % Filter coefficients
Afilt = filtfilt(h, 1, q.*exp(-1j*phi).');
figure();
plot(t, q, 'k');
hold on;
plot(t, abs(Afilt), 'r', 'LineWidth', 2);
grid on;
box on;
legend('q(t)', 'A(t)');
xlabel('s');
ylabel('Amp');
title('q(t) and A(t) - filtered');
set(gca,'FontSize',15);
xlim([1.2 1.8]);

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Kalasagarreddi Kottakota 2023-7-7

Hi @N A POORNA CHANDRA, I think there is a issue with this type of filtering. The result it produces is not even near to the result, I have shown in my question.

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