I'm not familar with the content of your question, but I hope the graphing improvements may help you diagnose. 'j' was undefined and I'm imagining it's some kind of damping coefficient. You might try different values to get optimal damping.
clear all
fs = 1;
f = linspace(-1,1,1e5);
j = 1;
s = j * 2 * pi * f/fs;
% System impluse response
Hs = 1 ./ (1 + 10^-6 .* s);
figure
plot(f, Hs)
title('System Impulse Response')
xlabel('f')
ylabel('H(s)')
% Rectangular wave spectrum
Tm = 150 / fs;
T = Tm / 2;
Sinc = Tm * sin(2 * pi * T .* f./fs) ./ (2 * pi * T .*f ./fs);
figure
plot(f, Sinc)
title('Rectangular Wave Spectrum')
xlabel('f')
ylabel('sinC')
% Rectangular wave spectrum shifted T in time domain
Xrec = Sinc .* exp(-j * T * pi .* f./fs);
figure
plot(f, Xrec)
title('Rectangular Wave Spectrum')
subtitle('Shifted T in Time Domain')
xlabel('f')
ylabel('Xrec')
% Convolution of Hs and shifted rectangular in frequency domain
Output = conv(Xrec, Hs, 'same') .* (f(2) - f(1));
figure
plot(f, Output)
title('Convolution of Hs and Shifted Rectangular in Frequency Domain')
xlabel('f')
ylabel('Output')
