Wrong FFT for an audio file

Question

Amirhosein Khanlari 2020-1-21

0
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此问题的直接链接

https://ww2.mathworks.cn/matlabcentral/answers/501357-wrong-fft-for-an-audio-file

评论： Star Strider 2020-1-26

v0.mp3.zip

I want to sketch the power spectrum of an audio file but i get wrong answer.human speech should be in range of 50 to 300 hz

[x Fs] = audioread('v0.mp3');
nf=length(x);
Y = fft(x,nf);
Y = Y-mean(Y);
f = Fs/2*linspace(0,1,nf/2+1);
plot(f,abs(Y(1:nf/2+1)));

i should get this:

Screen Shot 2020-01-22 at 2.26.05 AM.png

but instead i get this:

Screen Shot 2020-01-22 at 2.26.39 AM.png

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Walter Roberson 2020-1-21

Why are you subtracting the mean() of the fft from the fft results? It would make a lot more sense to have subtracted the mean of x from x

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Answer 1

Star Strider 2020-1-21

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https://ww2.mathworks.cn/matlabcentral/answers/501357-wrong-fft-for-an-audio-file#answer_411314

在 MATLAB Online 中打开

The plot is correct. You are not considering the exponential multiplication at the right end of the frequency axis.

This makes it a bit more obvious:

[x Fs] = audioread('Amirhosein Khanlari v0.mp3');
nf=size(x,1);
Y = fft(x-mean(x))/nf;
f = Fs/2*linspace(0,1,fix(nf/2)+1);
figure
plot(f,abs(Y(1:nf/2+1))*2)
xlim([0 1.5E+4])
set(gca, 'XTick', (0:2500:15000))

producing:

1Wrong FFT for an audio file - 2020 01 21.png

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Amirhosein Khanlari 2020-1-26

在 MATLAB Online 中打开

if i use the power the maximum code wont work:(

[x Fs] = audioread('Amirhosein Khanlari v0.mp3');
nf=size(x,1);
Y = fft((x-mean(x)).^2)/nf;
f = Fs/2*linspace(0,1,fix(nf/2)+1);
[maxAmp,maxAmpidx] = max(abs(Y(1:nf/2+1))*2);           % Maximum Amplitude & Index
figure
plot(f,abs(Y(1:nf/2+1))*2)
xlim([0 1.5E+4])
set(gca, 'XTick', (0:2500:15000))
text(f(maxAmpidx), maxAmp, sprintf('\\leftarrow %.1f Hz = %.5f Amplitude', f(maxAmpidx), maxAmp), 'HorizontalAlignment','left')

Star Strider 2020-1-26

在 MATLAB Online 中打开

That is interesting. Subtracting the mean should produce a zero D-C offset. It does in the Fourier transform, however it does not when the time-domain signal is squared first.

According to Parseval’s Theorem, it is correct to square the Fourier transform or the original time-domain signal. Squaring the Fourier transformed signal to create ‘Psd’:

[x Fs] = audioread('Amirhosein Khanlari v0.mp3');
nf=size(x,1);
Y = fft(x-mean(x))/nf;
f = Fs/2*linspace(0,1,fix(nf/2)+1);
Psd = (abs(Y(1:nf/2+1))*2).^2;
[maxAmp,maxAmpidx] = max(Psd);              % Maximum Amplitude & Index
figure
plot(f,Psd)
xlim([0 1.5E+4])
set(gca, 'XTick', (0:2500:15000))
text(f(maxAmpidx), maxAmp, sprintf('\\leftarrow %.1f Hz = %.2E Amplitude', f(maxAmpidx), maxAmp), 'HorizontalAlignment','left')