frequency vector in a fft

Question

SYML2nd 2019-6-13

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此问题的直接链接

https://ww2.mathworks.cn/matlabcentral/answers/466872-frequency-vector-in-a-fft

编辑： Daniel Frisch 2020-8-31

cc.txt

Hi all,

I am trying to do the fft of a signal (here attached cc.txt), unfortunately I do not understand which frequency I should associate at each value of the fft, in other word I did not understand how to create the frequency vector. I have tried to apply what I've read here https://it.mathworks.com/help/matlab/ref/fft.html and I have done this code, but unfortunately the frequency vector and the fft have different lenght, so an error results.

Can you help, what I am doing wrong in this code and why???

Thank you in advance

cc1=readtable('cc.txt')

cc=table2array(cc1(:,2:2))

L=length(cc)

ccf= fft(cc)

Tinc=0.001

Fs=1/Tinc

fn=Fs/2

L=length(cc)

f = Fs*(0:(L/2))/L;

plot(f,ccf)

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Answer 1

Star Strider 2019-6-13

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https://ww2.mathworks.cn/matlabcentral/answers/466872-frequency-vector-in-a-fft#answer_379015

在 MATLAB Online 中打开

Try this:

plot(f,ccf(1:numel(f))*2)

That should do what you want. (It plots the ‘positive half’ of the fft result, from D-C (0 Hz) to the Nyquist frequency, and the correct amplitude, multiplying the returned amplitude by 2.)

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Answer 2

SYML2nd 2019-6-13

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https://ww2.mathworks.cn/matlabcentral/answers/466872-frequency-vector-in-a-fft#answer_379054

First of all thank you for your answer. But I have still doubts?

So was my frequency correct?

I didn't get why you multiplied the returned amplitude by 2

So, doing

ccf(1:numel(f))

am I am taking just part of the fft (from the first to the lenght of the f vector)?

Am I discarding a part of the fft because it exceeds the Nyquist limit?

Thank u in advance

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Star Strider 2019-6-13

The Fourier transform output represents both the ‘positive’ and ‘negative’ frequencies (on either side of 0 Hz), so the energy is equally divided between the two sides. Multiplying by 2 corrects for this and approximates the amplitude of the time-domain signal.

Am I am taking just part of the fft (from the first to the lenght of the f vector)?

Am I discarding a part of the fft because it exceeds the Nyquist limit?

Exactly. It actually does not exceed the Nyquist frequency (although that is the maximum frequency you can uniquely represent in a sampled signal). It instead eliminates the mirror-image negative half of the fft output. You can see this by constructing an appropriate frequency vector, then using fftshift on both the frequency vector and the fft output. If ‘Fn’ is the Nyquist frequency, the result of the fftshift function will plot the fft output from -Fn to +Fn.

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