in mathematics, the inverse operation of convolution signals. In general, the purpose of deconvolution is to find solutions of the convolution equation defined as: f * g = x. Where h is the recorded signal, and f is a signal that you want to recover, and we know that the first signal is obtained ...

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How does scipy.signal.deconvolve work?

The deconvolve(signal, divisor) function of scipy ...
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67 views

Signal enhancing algorithm (deconvolution??)

I need an algorithm (preferably Pascal-like, but anything else will do it also) that will make the "signal" (actually a series of data points) in left look like the one in right. Signal origin: ...
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The graph obtained from my deconvolution routine seems to be shifted, is that supposed to happen that way?

So I'm writing a piece of code to deconvolve pseudo-data obtained from a (slightly)blurry particle-detector, using the gold algorithm of deconvolution. But the strange thing is, the graph I obtain ...
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18 views

Impulse response from basis functions with initial zero response

I have a system where I am applying a unit surface step function and measuring a subsurface output. This means I have zeros in the response until the disturbance reaches the sensor. I need to find ...
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19 views

Intuitive understanding of 2d deconvolution vs convolution of images in CNNs

I'm looking for an intuitive understanding of the deconvolution mechanism to upsample reconstruct images / upsample feature layers as explained in the work of Mathew Zeiler here and here. I found an ...
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23 views

Why is the term deconvolution used more for signals and not so much (or at all) for systems?

Wikipedia defines mathematical deconvolution here, and with the examples given and my experience, what I've read over the years is that deconvolution is used to determine an input signal provided a ...
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1answer
42 views

How to deconvolve matrix when a model of noise exists?

I have a matrix of N rows of time-series data. There is a specific noise contaminating measurement of the data that I have some information about. The noise in the data can be modeled as a poisson ...
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1answer
92 views

Compensating Loudspeaker frequency response in an audio signal

I have been working on a project in which I was required to work on the audio signals recorded from the loudspeaker kept in front of a filter. So, to simply explain it: $$\boxed{\rm LoudSpeaker} \...
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18 views

concerning the usable frequency band of signal

The spectrum amplitude of the response of instruments is generally trapezoid-shaped, with a flat portion in the middle and decaying at higher and lower frequencies. By deconvolving with the ...
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48 views

how to get an input test signal for convolution/ distortion method

i am trying to do some experiments with Total Harmonic Distortion. According to ...
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35 views

Why sparse prior like total variation opts to concentrate derivatives at a small number of pixels?

When performing image deconvolution (deblurring), people often make use of priors to get rid of the illness of the problem. One very common prior is total variation, a sparse prior. Compared to ...
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Why do we assume the matrix of impulse responses to be a Toeplitz matrix during deconvolution

$y(n)$ = output signal $x(n)$ = input signal $\mathbf H$ = system response as a toeplitz matrix $$\mathbf H = \begin{bmatrix}h(0)&&&\\h(1)&h(0)&&\\h(2)&h(1)&h(0)&\...
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How to use deconv() instead of roots() on MATLAB to find roots to a polynomial [closed]

I recently read that for polynomials of degree 5 or more, when executed with the roots() command on MATLAB produces an error. The documentation said as follows: As a substitute, using the deconv() ...
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52 views

How can convolution and deconvolution be defined for 3D images?

I am trying to understand how convolution and deconvolution can be represented for 3D images/ stacks of data. I would prefer it, if you built the these concepts from 1D vectors to 3D matrices in terms ...
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11 views

How to remove roots at z=1 by using pdiv function in scilab?

I'm trying to write a code for line spectral frequencies from prediction filter coefficient and I have two polynomials P1 and Q1 as arrays from which I have to remove the known roots at z=1 and z=-1(...
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26 views

What are the figures of merit/ performance measurements I can use for deconvolution?

I'm currently performing deconvolution on a bunch of 2D slices of fluorescent beads using MATLAB. Now I want to measure the performance of different deconvolution methods on the filtering of the PSF(...
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78 views

Determining channel frequency response from measured data via IFFT

I've been working on a small system that transmits a linear chirp over the 35Hz-20kHz frequency range in a room and simultaneously records the transmitted signal with echoes (from the floor, walls, ...
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33 views

Enforcing size to match Convolution using 'same' property & Enforcing Circulant Matrix (Like DFT Based Convolution)

The original problem was from this link about coding de-noising an audio signal. Because my reputation points disabled me to comment, I have to ask a separate question here. I don't quite ...
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702 views

Use MATLAB to restore the signal from a given degraded signal using Tikhonov regularization

Anyone could share how to develop an application in MATLAB to restore the signal from a given degraded signal using Tikhonov regularization i.e restoring the signal $f$ via solving $$ \min || g - f ...
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414 views

Deconvolution in Python in 2D

Referring to this topic, I am interested in a deconvolution using Python. However, unlike the linked topic above, I want to deconvolve a 2D image. The scipy.signal.deconvolve function unfortunately ...
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70 views

Convolution theorem for “weighted” convolution?

Consider what I call a "weighted" convolution of a two-dimensional signal (image) with itself: $f({\bf r}) = \int d {\bf r}' \, g({\bf r}') s({\bf r},{\bf r}') g({\bf r}-{\bf r}')$ where $s$ is a ...
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35 views

Fourier domain division causing translation

I am trying to find the correct filter to convolve with an image so they have the same PSF. I have the final PSFs of both images: A: PSF of the image with the wider PSF. B: PSf of the image with ...
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1answer
86 views

Deconvolution using response to an Heaviside

I'm measuring a "charge" signal in function of time from an amplifier. Here is a measured signal (x-axis is the time in some arbitrary units, y-axis is the charge in ADU): I would like to get the "...
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25 views

Isolating overlapping image

Using a diffraction grating in front of my smartphone's camera, I can decompose light sources into their spectral components. The problem is that the background is not always dark and there might be ...
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82 views

Extracting original signal from overlapping area

Considering this image, where I have a spectral decomposition of a light bulb. Due to the non point shaped light source, the spectral decomposition using a diffraction grating in front of my camera ...
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153 views

1-D deconvolution in Matlab

Suppose that I know the output and the transfer functions of a system and I would like to calculate the input function using deconvolution. To get a grasp of the idea I have created a simple ...
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156 views

Deconvolution of signal which is broadened by laser spot size

I have a signal that I measured by optical means using a focused laser. The laser scans over a microscopic feature (in step size of 0.33 micron) and I have plotted the result of the measurement as a ...
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90 views

Sharpen defocused image

Using OCR, I want to extract text from product packages using Google Glass. However, because of the fixed focus of the camera the package pictures are blurred. Is there a way to sharpen the image? ...
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147 views

Increasing the number of points in the frequency spectrum

I have an image with few pixels in length and height. For this image I calculated the two dimensional Fourier transformation. What I got for the frequency spectrum in one direction was a very ...
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1k views

What does it mean to deconvolve the impulse response

I am learning DPS and I came across the problem of deconvolution and removing the impulse response from a signal? This still does little sense to me. My understanding of the impulse response is to ...
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58 views

Multi-image denoising

I have two signals Sa and Sb, both affected by the same noise. I don't know how much noise is mixed into each one, and the signal+noise is transformed using some (unknown) nonlinear function before I ...
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77 views

Are convolution and deconvolution kernel the same?

I need to clarify this and rather confused by this. Lets say: $x = h * g$ $x$ - measured data $h$ - raw data $g$ - instrument response function (convolution kernel) So lets say I ...
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336 views

Prove that time-reverse yields inverse filter for deconvolution?

In reading literature on the construction of impulse responses from sine sweeps (e.g. papers by Farina), I see it stated over & over that the way the impulse response is constructed from a (...
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158 views

Problem implementing deconvolution to recover an Impulse Response

I’m new to DSP programming and I’m trying to learn a bit about convolution and deconvolution and FFTs. I have a project where I am taking a signal (a sine sweep) and convolving it with a shorter ...
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How to perform Wiener deconvolution in Matlab

I have an output signal $y$ which is an input signal $x$ convolved $\star$ with an impulse response function $h$ with some added noise $n$ : $$y(t) = h(t) \star x(t) + n(t)$$ I know the input signal ...
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1answer
42 views

How to extract unknown packet from collision between said packet and another, known packet?

I need to apply successive interference cancellation (SIC) to an RF signal which is the result of collisions between 2 or more unsynchronised packets. For this question let's just assume that the ...
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1answer
28 views

Available Online Recordings for Acoustic Echo Identifiablity

I am trying to add a few samples for a publication on identification of clean signal from the one which has echo on it. For this purpose I need data set that includes playback of an already available ...
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40 views

variation of the source separation problem

I have four sensors which make measurements $y_k(t)$ that can be modeled as complex time series: $y_1(t) = h_1(t) * x(t) + n_1(t)$ $y_2(t) = h_2(t) * x(t) + n_2(t)$ $y_3(t) = h_3(t) * x(t) + n_3(t)$...
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884 views

Deconvolution by convolution

This is now a second time I am attempting to ask this very important but simple question here. What I want to know is can you do deconvolution by convolving a signal. It is often stated that, for ...
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155 views

How to deconvolve dependent part of signal from independent part?

I have a problem of the following form. There are two signals, x(t) and y(t). The model for the system is such that: $$x(t) = x'(t) + f(y(t))$$ where $f(y(t))$ is a variable offset introduced by ...
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55 views

How to restore an image from its filter output?

I'm wondering if there is a way that I can reconstruct an image, given the output vector obtained from the convolution with a certain filter. For example I convolve my image with a filter from MR8 ...
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2answers
131 views

Conceptual questions from signal processing

I don't have a thorough background in Signal processing and require some information for an application pertaining to computer science. Minimum Entropy Blind Signal Deconvolution with Non Minimum ...
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1answer
355 views

Continuous-time mathematical formula for deconvolution filters

I have an elementary function $p:\mathbb{R}^2\rightarrow\mathbb{R}$ which (locally) represents an image. It's a polynomial, and its the result of the following 2D convolution: $$p=f\star G\star \...
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2D Deconvolution in matlab

I am trying to solve the following equation for h (an [MxM matrix]): $$ k[\tau_1,\tau_2]=\sum_{i_1=0}^M \sum_{i_2=0}^M h[i_1,i_2]x[\tau_1-i_1]x[\tau_2-i_2] $$ I have k, which is a 2D [MxM] symmetric ...
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116 views

How to create a convolution matrix with a variable condition number(CN)

I want to know the performance of a deconvolution algorithm with different CN, so I'm convolving my signal with different convolution matrices(different CNs) and then applying the deconvolution ...
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1answer
719 views

Relationship between Discrete Deconvolution and Toeplitz Matrices

I have 2 vectors, $a$ & $c$, both of length M. I know they are related by $a*b=c$. My goal is to recover $b$. Obviously $b=$deconv$(c,a)$. I am only interested in the first M elements of the ...
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84 views

Why is deconvolution used in telescopes, CT scans and seismographs?

Can you explain to someone with no mathematical background why is deconvolution used in telescopes, CT scans and seismographs? How do you explain that the same technique can be used for different ...
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239 views

How to calculate IDFT this signal? [closed]

$X(jw) = 1 + \frac {jw+3}{jw+4}$ what is the IDFT of this signal?
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111 views

How do you deconvolve irregularly sampled points?

$f:\mathbb{R}^2\rightarrow\mathbb{R}$ is an unknown signal, and $g:\mathbb{R}^2\rightarrow\mathbb{R}$ is a known point-spread function (in my particular case it's just a Gaussian). A system samples $...
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338 views

Is there a difference between the (image) kernel and point spread function when talking about deconvolution?

When you use the deconvolution method to make the blurry image sharper, you will have to estimate the Point Spread Function. Is there a difference between this PSF and an image kernel? Second ...