# Single sided spectrum through FFT algorithm

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Aishwarya Govekar on 18 Jul 2020
Commented: Aishwarya Govekar on 22 Jul 2020
I was trying to perform spectral analyis of speech signal. But can anyone please explain the meaning of those three lines which I have highlighted in Bold font? I got this code from somewhere online.
I have also attached the screenshots of the output graph and other output details ffor your reference. Kindly go through them.
Thank you.
l = length(data);
NFFT = 2^nextpow2(l);
f = fs/2*linspace(0,1,NFFT/2+1);
xf = abs(fft(data, NFFT));
subplot(2,1,1);
plot(data);
title('Input Speech Signal');
subplot(2,1,2);
plot(f, xf(1:NFFT/2+1));
title('Single Sided Spectrum of the Speech Signal');

Devineni Aslesha on 21 Jul 2020
Hi Aishwarya,
Here is the explanation for the lines highlighted in bold.
1. f = fs/2*linspace(0,1,NFFT/2+1);
2. xf = abs(fft(data, NFFT)); Here, abs(fft(data, NFFT)); should be abs(fft(data, NFFT))/l; as the fft result is generally divided by the signal length in order to scale it to the same total power as the time-domain signal.
fft is a method used to transform from the time domain to the frequency domain and gives a complex result. Since, spectrun is the distribution of the amplitudes and phases of each frequency component against frequency, we are using abs function to get the amplitude of each frequency component.
3. plot(f, xf(1:NFFT/2+1)); Here, xf(1:NFFT/2+1) should be 2*xf(1:NFFT/2+1).
To compensate analytically for the notion that no negative frequencies exist, the symmetrical negative frequency components are truncated using xf(1:NFFT/2+1) and the positive frequency components are multiplied by two instead.
Aishwarya Govekar on 22 Jul 2020
Oh okay... Thanks a lot for such a clear explaination!

R2019a

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