Signal analysis - need help with FFT

I have a signal that I'm trying to analyze using FFT and rectangular window. However I am not sure how to adjust the value of "t" and use rectangular window on this signal to perform correct analysis Can you please tell me what am I doing wrong? Thank you in advance.

clear
close all
clc

fs=2000;
T=1/fs;
t=0:T:(1-T);
y=sin(200*t.*sin(60*t));
% Plot signal
figure(1);
plot(t,y);
title('Signal');
xlabel('Time [s]');
ylabel('Amplitude');


% Spectrum
figure
widmo=(abs(fft(y)));
stem(widmo);
title('Spectrum')
grid on;
axis tight;
xlabel('Frequency [Hz]');
ylabel('Amplitude')

% Rectangular window

N = length(y);
w = window(@boxcar,fs);
okno = y.*w';
figure;
plot(t,okno);

figure;
bar(abs(fft(okno)));

[dpb]

First need to explain what you think you're trying to do...a rectangular window is the same as no window at all; it's simply included in the Matlab vocabulary for completeness.

BTW, boxcar is deprecated; if you must apply a pointless window, use rectwin instead (altho the result is still the same).

[Janusz Rogalski]

In my homework teacher wrote: perform spectral analysis (rectangular window). Are the values in code picked correctly? I think that this function is periodic but what do I need to do to get reasonable frequency values to describe this signal? Thank you for your help.

[dpb]

Well, being homework, we expect the student to do the work! :)

Do you understand the comment re: the rectangular window being the same as no window?

Are you sure that's really the signal you're intending? That's a most peculiar one, if so, and hardly conducive to a beginning exercise...

After you plotted it have examined its characteristics closely? (HINT: expand the x-axis markedly like w/ xlim([0 0.2]) )

Look at the example at

doc fft

for calculation of the FFT-based one-sided PSD normalized to yield the signal magnitude for a noise-free signal...there are several long threads I've written Answers to here on the forum over the last several months to year, perhaps, that expound on this subject at length.

[David Goodmanson]

Hi Janusz,

It may or may not be what was intended, but certainly the spectrum of

y = sin(200*t).*sin(60*t);

is a lot easier to interpret than the spectrum of

y = sin(200*t.*sin(60*t));

[dpb]

Ah! yes, a misplaced parentheis could make a big difference here! Good catch! :)