How to design a low pass filter with rectangular window?

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])

Answer 1

[N A POORNA CHANDRA]

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]);

[Kalasagarreddi Kottakota]

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.