# Questions tagged [convolution]

Convolution is a mathematical operation on two functions f and g, producing a third function that is typically viewed as a modified version of one of the original functions.

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### Proof for the energy correction factor of DFT

I am looking for a mathematical proof for the energy correction factor in conteext of windowed discrete fourier transform. In Spectrum and spectral density estimation by the Discrete Fourier transform ...
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I'm facing confusion about the definition of the convolution between two discrete periodic signals. Basically, the definition of convolution between s and ...
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### Convolution error when using DFT for non-periodic functions

I need help understanding why FFT-based computation of convolution on a finite domain, between two non-periodic functions often gets it wrong. Specific questions: (1) why does FFT-based computation ...
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### Comparing methods of blind source separation

I am currently working on blind source separation using sparse hypotheses and convolutive mixtures. For my project, I have compared three different methods and calculated the Signal-to-Distortion ...
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### How can Haar basis be written as the impulse response of an LTI system?

Haar wavelets are defined as: \phi_{0,0}(t) = \begin{cases} 1, & \text{ for } 0<t< 1/2\\ -1, & \text{ for } 1/2<t<1 \\ 0, & \text{ ... 1 vote
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### 3D convolution product with Fourier transforms, FFTW and MPI in C

My question is not really from the field of signal processing but I think you are the most suited for answering my question. I am willing to compute the gravitational potential which can be written as ...
1 vote
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### Effect of BIBO-Instability on the frequency response of a ideal LPF

I recently came across this post stating that the continuous ideal LPF is BIBO-unstable since the impulse response is not absolutely integrable, and this post stating some examples. I have been trying ...
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### Is downsampling LTI for bandlimited inputs?

This question stems from the discussion we had on a previous question of mine. The point of contention is whether the downsampling operator is time invariant or not. Which gives us a new condition to ...
1 vote
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### Is it possible to consider circular convolution in case of appending the guard interval as a suffix instead of a prefix

In OFDM system, the cyclic prefix is added into the head of time-domain signal to enable the circular convolution with the channel, and then perform one-tap frequency-domain equalization at the ...
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### Discrete convolution of a causal signal with a delayed unit step

I am computing the discrete convolution of a signal $x[n] = a^nu[n]$ with a delayed unit step, say $h[n] = u[n-5]$. If I place both directly into the discrete convolution formula I end up with: \$\frac{...