What is NFFT used in fft() function in matlab?

5
votes

I have a audio signal sample at the rate of 10Khz, I need to find fourier coefficients of my signal. I saw one example in mathwork's website where they are using following code to do the fft decomposition of a signal y: 

NFFT = 2^nextpow2(L);    
Y = fft(y,NFFT)/L;
f = Fs/2*linspace(0,1,NFFT/2+1);

where L is the length of the signal, I don't really understand why its defining the variable NFFT the way shown in the code above? Can't I just chose any value for NFFT? Also why are we taking Fs/2 in third line of the code above?

2
matlabsignal-processingfft
Last line should have been linspace(0, Fs/2, NFFT/2+1) -- what's the point of using the function that minimizes rounding error, and then introducing rounding error? - Ben Voigt

2 Answers

9
votes

NFFT can be any positive value, but FFT computations are typically much more efficient when the number of samples can be factored into small primes. Quoting from Matlab documentation:

The execution time for fft depends on the length of the transform. It is fastest for powers of two. It is almost as fast for lengths that have only small prime factors. It is typically several times slower for lengths that are prime or which have large prime factors.

It is thus common to compute the FFT for the power of 2 which is greater or equal to the number of samples of the signal y. This is what NFFT = 2^nextpow2(L) does (in the Example from Matlab documentation y is constructed to have a length L). When NFFT > L the signal is zero padded to the NFFT length.

As far as fs/2 goes, it is simply because the frequency spectrum of a real-valued signal has Hermitian symmetry (which means that the values spectrum above fs/2 can be obtained from the complex-conjugate of the values below fs/2), and as such is completely specifies from the first NFFT/2+1 values (with the index NFFT/2+1 corresponding to fs/2). So, instead of showing the redundant information above fs/2, the example chose to illustrate only the spectrum up to fs/2.

1
votes

Output of FFT is complex for real valued input. That means for a signal sampled at Fs Hz, The fourier transform of this signal will have frequency components from -Fs/2 to Fs/2 and is symmetric at zero Hz. (Nyquist criterion states that if you have a signal with maxium frequency component at f Hz, you need to sample it with atleast 2f Hz .

You may wonder what does negative frequency mean here. If you are a mathematician you may care about the negative frequency but if you are an engineer, you may choose to ignore the notion of negative frequency and focus only on frequencies from 0 to Fs/2. (Max freq component for a signal sampled at Fs Hz is Fs/2)

Using FFT to learn more about frequency components present in your signal is cumbsrsome. You can use the function pwelch function in MATLAB to learn more frequencies present in your signal and also the power of these signals. MATLAB will automatically compute the NFFT required and return the frequencies present in your signal along with the power at each frequency. Use this syntax:

[p,f] = pwelch(x,[],[],[],Fs)

Look at the documentation of pwelch for more information.