I can't make sense of the amplitude spectrum of a signal. Help please.
1 view (last 30 days)
Show older comments
Hi,
I have a sinusoidal signal namely:
signal = sin(2*pi*0.08*t) + sin(2*pi*0.2*t) + sin(2*pi*0.32*t) + sin(2*pi*0.4*t);
so the segment of the code becomes:
freqs = [0.08, 0.2, 0.32, 0.4];
periods = 1./ freqs;
% Let the max value of t be 4 times the largest period
t_max = 4 * periods(1);
% Let us have 500 samples over the interval [0, t_max].
t = linspace(0, t_max, 500);
% The synthesized signal
signal = sin(2*pi*0.08*t) + sin(2*pi*0.2*t) + sin(2*pi*0.32*t) + sin(2*pi*0.4*t);
Now I wanna view the amplitude spectrum for the first 50 samples.
So I did this:
signal_first_50_samples= signal (1:50);
% Display its magnitude spectrum.
N = 64;
signal_spect = abs (fft(signal_first_50_samples,N));
signal_spect = fftshift(signal_spect);
F = [-N/2:N/2-1]/N;
plot (F, signal_spect)
set(gca, 'XTick',[-0.5:0.1:1])
grid on;
I was expecting spikes at each of the frequencies, however, I got this:
can anyone help me understand?
Thanks
0 Comments
Accepted Answer
Image Analyst
on 7 Dec 2014
If the signal is 500 samples and has 4 periods, then each period is 125 samples long. If you take less than half that you probably don't have a long enough signal to get a reliable spectrum. You're trying to get a spectrum when some of the frequencies don't even have half a cycle in the signal. Why did you take just 50 and not the whole signal?
4 Comments
Image Analyst
on 7 Dec 2014
Looks like your sampling frequency is not enough to follow the curves exactly. But at least you're getting all 4 spikes now like you should. It appears that there is some effect of the overall, total sample length because I can see side lobes caused by the sinc function, which is what you will get when you truncate your signal by a rect function. If you had higher resolution and took more cycles, that effect would be less.
More Answers (0)
See Also
Community Treasure Hunt
Find the treasures in MATLAB Central and discover how the community can help you!
Start Hunting!