# Questions tagged [deconvolution]

For questions on deconvolution, the resolution of a convolution function into the functions from which it was formed in order to separate their effects.

34 questions
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### How does scaling in frequency domain affect real space?

I have a 3 dimensional array of real data corresponding to measurements in physical 3D space, and its corresponding data in spectral space. I want to scale certain specific frequencies in the ...
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### Verifying the results of Deconvolution using Residual Number System

I have been reading this paper and I think I understand it. However, I am not able to verify the example given at the end of the paper. To summarize, given matrices ...
1answer
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### Solving minimization problem $L_2$ IRLS (Iteration derivation)

In the article ''' Chartrand, Rick, and Wotao Yin. "Iteratively reweighted algorithms for compressive sensing." Acoustics, speech and signal processing, 2008. ICASSP 2008. IEEE international ...
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### Fredholm equation with unknown Kernel / De-convolution

I'm wondering if the following integral equation has any hope of an algebraic solution: $\frac{2}{(x-2)^2}=\int_0^{\frac{1}{2}} f(x-s) f(s) \, ds$, where $f(\cdot)$ is unknown. This is a Fredholm-...
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### Fourier Convolution Inversion

Consider a Fourier convolution $f(x) = (g * h)(x)$, where $g$ and $h$ are arbitrary but known functions with reasonable properties. Is there any possibility to determine the inverse function of this ...
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### Deconvolution and Polynomial factoring using the FFT

I've been trying to implement a general N dimensional deconvolver for various engineering applications and some math curiosities. For speed and simplicity I've decided to try and do this with help of ...
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### Curve Fitting Including Convolution in MATLAB

I would like to fit two parameters $K_1$ and $k_2$ in the problem $f(t)*C_a(t) = C_E(t)$ where $*$ represents the convolution operator and $f(t) = K_1 e^{-k_2 t}$. $C_a(t)$ and $C_E(t)$ are given ...
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### Deconvolution of two delta functions (solving $y(t) = A x(t-a) + B x(t-b)$)

I would like to calculate $x(t)$, when only $y(t)$ with $y(t) = A x(t-a) + B x(t-b)$ is known. Since this is a linear shift invariant operation (convolution), the inverse relation must be of the ...
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### Convolution/Deconvolution $\stackrel{?}{=}$ Coding/Decoding

In a strict mathematical sens, can a convolution/deconvolution be equivalent to a coding/decoding process ? I just got the remark from a reviewer that it's strictly different, it's a little surprising ...
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### Pseudo-inverse of an underdetermined Toeplitz matrix

I have an undetermined Toeplitz matrix (more columns than rows). For example: \begin{equation*} T = \begin{pmatrix} 1 & 1 & 1 & 1 & 1 & 0 & 0 & 0 & 0 ...
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### Can FFT be adapted for deconvolution of non-periodic functions?

Can a non-periodic function be padded at the boundaries and deconvolved with inverse FFT? Since a Toeplitz matrix can be embedded in a circulant matrix to perform the deconvolution, is there an ...
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### Decomposition of exponential random variable

I know that sum of independent Exponential random variables follows Gamma distribution. But Is it possible to decompose ...
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### How to choose a phase for the deconvolution of an autocorrelation?

Say I have a function, $C=C\left(x\right)$, whose fourier transform is denoted by $c=c\left(k\right)$, i.e. $C\left(x\right)=\sum_{k=-\infty}^{\infty}c\left(k\right)\chi\left(x\right)$, where \$\chi\...