# Tag Info

### I want to understand the fundamental difference/connection between DFS, DFT and DTFT

The Dirichlet Kernel and the Sinc Function are actually quite close as the number of samples get large (you can interpret, quite accurately, the Dirichlet Kernel as an aliased Sinc function). The ...
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### Power spectrum scaling conventions

The scaling of $\frac{1}{N}$ satisfies Parseval's theorem. The proof is pretty straightforward. We wish to show \sum_{n=0}^{N-1} \lvert x[n] \rvert^{2} = \frac{1}{N} \sum_{k=0}^{N-1} \...
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### Why do we care about the STFT of a signal?

If the signal is very very long, let's say it's minutes long, the spectrum at the end of the signal is likely to be very different from the spectrum at the beginning of the signal. Especially in audio,...

### Why Power of a signal of amplitude $A$ is $A^2$

I'll add a simple and intuitive explanation that augments the good details Hilmar has provided: Power is energy over unit time. Energy is the magnitude squared of the signal (in signal processing it ...
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### Is there a function whose Fourier transform gives peaks/impulse at multiple desired locations?

Yes any function that repeats in time will have a Fourier component at it's repetition rate, and if it's not a pure frequency but an arbitrary shape that is repeating, higher harmonics of that ...
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