MATLAB: Single sided spectrum of vector y obtained using fft

digital signal processingfftSignal Processing Toolbox

how to plot a single sided spectrum of vector y obtained using fft?

Best Answer

The way I usually calculate and plot it: 
t = linspace(0, 1, 1E+4);
s = sum(sin([0; 100; 200; 300]*2*pi*t*10)) .* randn*10;
Ts = mean(diff(t));                                         % Sampling Interval
Fs = 1/Ts;                                                  % Sampling Frequency
Fn = Fs/2;                                                  % Nyquist Frequency
L1 = numel(t);
FTs1 = fft(s)/L1;                                           % FFT Of Original Signal
Fv1 = linspace(0, 1, fix(L1/2)+1)*Fn;                       % Frequency Vector

Iv1 = 1:numel(Fv1);                                         % Index Vector

L2 = 2^nextpow2(L1);
FTs2 = fft(s,L2)/L1;                                        % FFT Of Zero-Padded Signal
Fv2 = linspace(0, 1, fix(L2/2)+1)*Fn;                       % Frequency Vector
Iv2 = 1:numel(Fv2);                                         % Index Vector
figure
subplot(2,1,1)
plot(Fv1, abs(FTs1(Iv1))*2)
title('FFT of Original Signal')
xlabel('Frequency (Hz)')
ylabel('Amplitude')
grid
subplot(2,1,2)
plot(Fv2, abs(FTs2(Iv2))*2)
title('FFT of Zero-Padded Signal')
xlabel('Frequency (Hz)')
ylabel('Amplitude')
grid
This also demonstrates a way to increase the frequency resolution of the fft result by zero-padding it.
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