Single sided spectrum through FFT algorithm

Question

Aishwarya Govekar 2020-7-18

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此问题的直接链接

https://ww2.mathworks.cn/matlabcentral/answers/566937-single-sided-spectrum-through-fft-algorithm

评论： Aishwarya Govekar 2020-7-22

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.

Please reply asap.

Thank you.

[data,fs] = audioread('BabyElephantWalk60.wav');

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');

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Answer 1

Devineni Aslesha 2020-7-21

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链接

此回答的直接链接

https://ww2.mathworks.cn/matlabcentral/answers/566937-single-sided-spectrum-through-fft-algorithm#answer_468612

Hi Aishwarya,

Here is the explanation for the lines highlighted in bold.

1. f = fs/2*linspace(0,1,NFFT/2+1);

https://www.mathworks.com/matlabcentral/answers/166697-plot-single-sided-amplitude-spectrum

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.

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Devineni Aslesha 2020-7-22

Hi Aishwarya,

f = fs/2*linspace(0,1,NFFT/2+1);

For the above line, the answer is Yes. If you go through the link provided in the answer, the explanation is "The positive half of the spectrum (NFFT/2 +1 gives this, including 0 and nyquist, hence the +1) is mapped onto your real frequencies from the 'normalised frequency'.

plot(f, xf(1:NFFT/2+1)); Here, xf(1:NFFT/2+1) should be 2*xf(1:NFFT/2+1).

The positive frequencies are multiplied by 2 since Matlab FFT returns double-sided, half the input energy is in each the positive and negative frequencies. Here is a similar question that might help you to understand more.

Aishwarya Govekar 2020-7-22