How to plot convolution between signal and Hilbert tranform operator

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Hi... I ask to reproduce the complex signal as a result from convolution between cosine wave and hilbert transform operator as a figure. I do the script as below, but then i confuse how to separate imaginary and real part signal. Can anyone help me?
t=0:0.01:1;
f=2;
omega=2*pi*f;
y=cos(omega*t);
%signal
h=1./(pi*t);
cs=conv(y,h);
% plot data
subplot (3,1,1)
plot (t,y)
subplot (3,1,2)
plot (t,h,'-r')
set(gca, 'XAxisLocation', 'origin', 'YAxisLocation', 'origin')
box off
subplot (3,1,3)
plot (t,cs)

Answers (1)

Sufiyan
Sufiyan on 27 Apr 2023
Hi,
You can refer to the code below.
t = 0:0.01:1;
f = 2;
omega = 2*pi*f;
y = cos(omega*t);
h = [Inf, 1./(pi*t(2:end))];
cs = conv(y,h);
% Plot
subplot(3,1,1)
plot(t,y)
xlabel('Time')
ylabel('y(t)')
title('Input Signal')
subplot(3,1,2)
plot(t,h,'-r')
xlabel('Time')
ylabel('h(t)')
title('Impulse Response')
subplot(3,1,3)
t_cs = linspace(0,2,length(cs));
plot(t_cs,real(cs),'b')
hold on
plot(t_cs,imag(cs),'r')
xlabel('Time')
ylabel('cs(t)')
title('Real and Imaginary Parts')
legend('Real','Imaginary')
hold off
Hope this helps!

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