# 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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### Create an input so that poles show up as outputs?

Let's say we have a rational, causal, stable LTI system with transfer function $$H(z) = \frac{A(z)}{B(z)}$$ If $H(z)$ has $N$ poles, we can in theory have only 1 of those poles, $p_i$, show up at the ...
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### Convolution between two unequal length vectors

Considering an example, where the model is \begin{align} x[n] = \mathbf{h}^\mathsf{T}\mathbf{u}[n] + w[n]. \label{Eq1} \end{align} $\mathbf{h} = [h_0,h_1,\ldots,h_{M-1}]^\mathsf{T}$ of length $M$ ...
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### Where does convolution fit into tracking fluorescent photons using MC models?

I have been reading this old paper by Steven Jacques, a titan in the world of using Monte-Carlo methods for photon propagation and distributions. https://www.osapublishing.org/ao/abstract.cfm?uri=ao-...
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### How to calculate multiplication of two discrete series

Short version: How to multiply two discrete sequences? Long version: Convolution of two discrete sequences is weighted sum. For instance, convolution of two sequences: ...
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### why exponential term neglected in equation?

where does that exponential term gone, is this because it is a constant term or it has to do something with stablity?
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### Question on LSI system

Why second option (1) is not correct ?
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### Are convolution and multiplexing synonymous?

Other than preferences to use one or the other words in different domains, do they refer to essentially the same process? And likewise for the opposite operations, demultiplexing and deconvolution?
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### Convolution of even functions is even

Prove that the convolution of two even functions is an even function. I have my own proof which I have included as an answer, but it assumes a linear time-invariant system. I want to know if there is ...
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### Circular convolution of length L of sequences of length greater than L

I'm trying to understand how may I obtain the circular convolution of length L when the sequences I'm trying to convolve are of length greater than L. For instance this Matlab code using sequences ...
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### 2D Convolution in MATLAB Causes Artifacts (Boundary Issues)

I`m trying to do a 2D fast convolution in Matlab of large matrices. If I use FFT version based on convolution theorem ( https://en.wikipedia.org/wiki/Convolution_theorem ), there are some artefacts in ...
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### How to “scale” the FFT when using it to calculate discrete convolution?

As you probably know, the discrete convolution $H = F \ast G$ of some $F \left[ x \right]$ and some $G \left[ x \right]$ can be calculated using the Fast Fourier Transform (FFT). To do this, ...