define an interval for frequency of STFT outputs

Question

As you know the STFT has a matrix result, with the dimension given by:

number of frequency bins * number of time frames. 

For example, suppose that I have a signal with characteristics and I want to apply STFT method with the following input parameters:

• sampling rate : 250,000 Hz;
• data length : 498900 samples;
• window length : nftt=625 samples;
• hop size : 125 samples

With those parameters my STFT will have an output with size: 313*3987 (the method to calculate these values exists in some websites)

Now, my question is how can I define a limit for frequency dimension of STFT output? I think I should calculate my threshold values as an index number in STFT output, if so, how can I do it?

I have the frequency resolution, but when I multiply it by nfft, it's half of the value of sampling rate.

Answer 1

You haven't provided how you calculated the frequency resolution, but here is what it should be:

frequency_resolution = sampling_rate / nfft;

In your particular case with a sampling rate of 250,000Hz and nfft=625, this should give you a frequency resolution of 400Hz. You can verify that 625*400 is indeed equal to 250000.

Then, if you want to include frequencies from 0Hz to frequencies no greater than max_frequency as part of your STFT output, the maximum size along the frequency axis should be given by:

size_frequency_axis = 1 + floor(max_frequency / frequency_resolution);

As a special case you can also verify that when max_frequency is set to the Nyquist frequency (250000/2 = 125000), the computed size is 1+floor(125000/400) = 313 (which matches your full spectrum STFT output size).

As a generalization, if you want to include a range of frequencies not starting at 0Hz, then you can compute in a similar fashion the index of the minimum and maximum frequencies, and obtain the corresponding size with:

min_frequency_index = 1 + floor(min_frequency / frequency_resolution);
max_frequency_index = 1 + floor(max_frequency / frequency_resolution);
size_frequency_axis = max_frequency_index - min_frequency_index + 1;