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Phase extraction from Fourier transform

You need to evaluate the DFT at the frequency of the input signal. I recommend doing this experiment with the DTFT instead of the DFT. You can implement it in just a few lines of code, and unless the ...
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FFT of a gaussian signal in Python

There are two issues: The time axis is not long enough to capture a sufficient length of the Gaussian. The FFT is not properly scaled. For the first item mentioned regarding the time axis, the ...
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3 votes

Can anyone explain how dft works as a filter bank?

To add to Richard's good answer, I specifically want to show the difference between: Down-conversion and low-pass filtering (heterodyne the signal). Bandpass filtering the signal directly (...
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Can anyone explain how dft works as a filter bank?

@Ahmet. The DFT equation you posted does not compute an array of complex numbers. For any single given integer value of frequency-domain index $k$ the equation tells us how to compute the single ...
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1 vote

Bandwidth visualization in frequency domain

As a complement to Dan's answer: don't think in terms of the bandwidth per sample; this concept makes no sense. I recommend studying the discrete-time Fourier transform (DTFT) before the DFT. If you ...
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Bandwidth visualization in frequency domain

The length of the DFT is equal to the length of the time samples used ($N$ samples in time results in $N$ samples in frequency), and this frequency corresponds the the frequency range from $f=0$ to $f=...
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1 vote

Lowering Spectral Resolution of FFT

As @MBaz says in the comments, just do: ...
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What Does "Reduced Modulo N" mean in this context?

It just means that the number in the double parentheses is changed to be between $0$ and $M-1$ by adding to or subtracting from it $M$ an integer number of times. See equation (5) of the paper: $$ \...
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Sparse signal FFT

Partial FFT Sparse FFT Can also subsample the input, which will alias (fold) the high frequencies onto lower, then take FFT at the lower length, and then shift the result back onto higher frequencies ...
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