How to derive the bin width / maximum frequency of DFT/STFT

1. How do you calculate DFT frequency?
2. How do you calculate frequency bin in FFT?
3. What are the bins of a DFT?
4. How many frequency bins are generated by the FFT?

How do you calculate DFT frequency?

calculate the magnitude of each DFT output bin: magnitude = sqrt(re*re+im*im) find the bin with the largest magnitude, call its index i_max . calculate the equivalent frequency of this bin: freq = i_max * Fs / N , here Fs = sample rate (Hz) and N = no of points in FFT.

How do you calculate frequency bin in FFT?

The FFT provides amplitude and phase values for each bin. The bin width is stated in hertz. The bin width can be calculated by dividing the sample rate by the FFT length; or by dividing the bandwidth by the number of bins (which is equal to 1/2 the FFT length).

What are the bins of a DFT?

The DFT output frequency bins correspond to the frequencies Fk=kFsN. With the more common frequency axis of half positive, half negative frequencies, the frequency bins for a DFT are given by f=np. arange(-Fs/2, Fs/2, Fs/N) . In this case, an fftshift of the DFT output is required before plotting the result.

How many frequency bins are generated by the FFT?

FR = Fmax/N(Bins)

With a 1024 FFT size, we divide this band into 512 bins.