How to calculate the num_fft value?

Question

can you guys help me about this code,

fs = 1000

num_fft = 1024;


t = np.arange(0, 1, 1/fs)

f0 = 100
f1 = 200
x = np.cos(2*np.pi*f0*t) + 3*np.cos(2*np.pi*f1*t) + np.random.randn(t.size)


Y = fft(x, num_fft)
Y = np.abs(Y)


ps = Y**2 / num_fft

...

i found this code in internet, i do not understand what is the pupose of 'num_fft' in that code? and how to get the value? in the code above, here is worth 1024.

hope you can help me and thank you for all the help.

Answer 1

If you're using the FFT implementation in numpy (numpy.fft.fft) then the significance of num_fft is the length of the transformed axis of the output. In the context of FFTs this is the number of samples in frequency space.

Since your t (and consequently x) contains 1000 samples (as dictated by fs here), this num_fft value ends up padding your input with zeros to be 1024 samples long. If your x array was larger than 1024 samples, it would truncate the frequency space output to be equal to 1024 samples.

Depending on the library used for computing the FFT, this can have performance implications when your number of samples is not a power of 2. Most libraries nowadays used mixed-radix decimation in time so it's not a big concern, Try benchmarking the performance and you'll see if it affects you.

Here is the documentation.