# How to design a low pass filter with rectangular window?

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Kalasagarreddi Kottakota am 7 Jul. 2023
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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### Antworten (1)

N A POORNA CHANDRA am 7 Jul. 2023
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 am 7 Jul. 2023
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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