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Trying to plot frequency spectrum from set of samples.

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Hi everyone. I have a set of samples (x(n)'s) in a table corresponding to a mysterious signal x(t). What I am trying to do is display the frequency spectrum of this set of samples with a certain resolution.
I am confused on how to actually plot this frequency spectrum when I am just given a table of values, an fs, and using a certain N value.
So for example, say I was given a set of samples like this:
0 1 2 3 4 5 6 7 8 9 0 1.25 0.57 -0.29 -0.78 -0.70 0.37 0.87 0.49 -0.18
How would I plot the frequency spectrum with say a resolution of 50 hz?
I went about it like this, (keep in mind this code pertains to a set of samples that is 1251 long, I created the above example for ease of use), however my graph doesn't look right as the magnitudes shouldn't go above 1 since the amplitudes never go above 1?
signal = xt;
N = length(signal);
fs = 25000; % 25000 samples per second
fnyquist = fs/2; %Nyquist frequency
plot(abs(fft(signal)))
xlabel('Frequency Spectrum)')
ylabel('Magnitude');
title('Double-sided Magnitude spectrum');
axis tight
  1 Comment
Amirmahdi Matin
Amirmahdi Matin on 18 Mar 2020
how to realize main component frequencies and their amplitudes of this signal ??

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Accepted Answer

Star Strider
Star Strider on 5 May 2015
‘So for example, say I was given a set of samples like this:’
‘0 1 2 3 4 5 6 7 8 9 0 1.25 0.57 -0.29 -0.78 -0.70 0.37 0.87 0.49 -0.18’
‘How would I plot the frequency spectrum with say a resolution of 50 hz?’
You would do it with the absolutely clear code between the first two figures in the documentation for the fft function.
This is essentially an exact copy of that code, other than its using your vector and sampling frequency:
x = [0 1 2 3 4 5 6 7 8 9 0 1.25 0.57 -0.29 -0.78 -0.70 0.37 0.87 0.49 -0.18];
Fs = 50;
Fn = Fs/2;
Fx = fft(x)/length(x);
Fv = linspace(0, 1, length(x)/2+1)*Fn;
Iv = 1:length(Fv);
figure(1)
plot(Fv, abs(Fx(Iv)))
grid
xlabel('Frequency (Hz)')
ylabel('Amplitude')

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