# sampling and FFT of a sinusoid signal

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Yian Chen on 26 Sep 2021
Commented: Chunru on 27 Sep 2021
There is a 50HZ sinusoid signal g(t)=sin(2*pi*50*t) where 0≤t<0.1 and it is sampled at a rate of 250HZ, how can I plot this signal and 25 samples defined from 0-0.1s but does not inlude 0.1s? And how can I get the magnitude spectrum and phase spectrum of this signal?

Chunru on 27 Sep 2021
f0 = 50;
fs = 250;
t = (0:1/fs:(0.1-.5/fs)); % [0, 0.1)
g = sin(2*pi*f0*t);
plot(t, g);
L = 512
L = 512
Y = fft(g, L); % compute spectrum, FFT length = 512
f = fs*(0:L-1)/L;
figure
subplot(211); plot(f, abs(Y)), title('Amplitude plot')
subplot(212); plot(f, (angle(Y))), title('Phase plot')
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Chunru on 27 Sep 2021
t = (0:1/fs:(0.1-.5/fs)) means the time t starting from 0, with interval of T=1/fs, and eding at half-sample interval before 0.1 sec (to ensure that 01. is not included. Therefore this ensures t in in [0, 0.1).
In order to compute spectrum, you need to do FFT. By default fft(x) will take Fourier Transform with the number of frequency points equat to the data points (in your case it is 25). To have a smoother plot of the spectrum, we can use larger number of NFFT points, there fore we use FFT length = 512 above.