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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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Convolution in image processing ?

I got the concept of Convolution in signal processing from a video lecture that it is method to get the area overlapped between two signals when one signal is flipped over and traversed over another ...
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Help Understanding Convolution Filter Formulation

I'm reading Computer Vision: Algorithms and Applications wich is available online as a PDF and on Chapter 3.2 page 111 it introduces convolution operators for images giving the formulation: $g(i, j) =...
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How to Deduce a Linear System's Impulse Response from a Set of Input and Output Signals?

I want to know how to solve those types of problems.. is it by inspection ? Consider the linear system below. When the inputs to the system $x_1[n]$, $x_2[n]$ and $x_3[n]$, the responses of the ...
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How to properly perform convolution on bitmap image?

Correct me if I'm wrong, I should read bitmap into matrix of float values where I would get numbers up to little more than 16*10^6, then I should expand my image matrix to size 2^k putting the ...
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Circular and Linear Convolution

What is the difference between circular and linear convolution? When would I choose one over the other? In image processing where a filter is applied to an image with a mask which type of convolution ...
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Breaking a convolution into smaller pieces

For a project I need to do convolution and i use gpu for calculations. Sometimes I have to deal with kernel sizes of 50x50 and this size of kernel is sufficiently large that it chokes the gpu. (not ...
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Covolution of DTFT [duplicate]

Possible Duplicate: Convolution and DTFT $x_1(n)=x_2(n)=1$ where $0 ≤ n ≤ N-1$ 1)The linear convolution of the signal gives a triangle how you write it in mathematical form? The DTFT of the ...
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Flipping the impulse response in convolution

During convolution on a signal, why do we need to flip the impulse response during the process?
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Applying a filter kernel defined by a continuous equation in the frequency domain

I have a filter kernel $K(\omega)$ completely defined in the frequency domain as a continuous function of angular frequency $\omega$. I know $K(\omega)$ defined as a continuous mathematical equation. ...
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Where to get the Kodak PhotoCD raw image dataset?

I've been doing some background reading on demosaicing raw images. I've seen the Kodak PhotoCD raw image dataset mentioned in a few papers on demosaicing: Image Demosaicing: A Systematic Survey High ...
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Decoding Matrix Encoded Surround Sound Through Convolution

I wish to create a finite impulse response filter to decode a dolby digital matrix encoded 2 channel signal into 5 channels. These filters would then be used in a realtime pipeline on a Linux machine ...
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What is the physical meaning of the convolution of two signals?

If we convolve 2 signals we get a third signal. What does this third signal represent in relation to the input signals?
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Understanding the frequency scale of a spectrogram

The graph below was derived from a raw seismogram recorded during an earthquake over a timespan from t=0 to t=1400 seconds (not shown on x-axis). The original seismogram $s(t)$ is not shown, but it ...
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Verifying the computation of a convolution

I have an input signal $$x(n)=\left(3,-5,4,3,-1,-2,6,8\right), n=-3,..,4$$ and impulse response $$h(n)=(1,-1,1,-1,1), n=-1,...,3.$$ The convolution between $x(n)$ and $h(n)$ is $$x(n)*h(n)=\sum_{-\...
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Linear predictive model convolution

Accidentally asked this question in the general area and was told to ask here, so... I've been trying to develop a lightweight, relatively-fast-to-decode sound compression format for use in my gaming ...
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Why idft(dft(a) * dft(b)) not equal to convolve(a, b)?

I'm a little confused... I always thought the DFT of a convolution was equal to a product of DFTs, but when I tried this in Python: ...
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Convolution involving turning each pixel value to the most represented pixel value of the neighbourhood

In order to correct gradual changes of intensities in the background of grey-scales images, I have been blurring them and then subtracting the original images from the convolved one. In some cases, I ...
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How do I implement the 3D structure tensor in C/C++?

I am trying to figure out the details on how to implement the 3D structure tensor in C/C++ in an easy but efficient way and need some advice! For a discrete function $ I(x_i,y_j,z_k)$ the 3D ...
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Convolving two signals

I saw a video where this guy used a program to do a frequency analysis on a voice signal and a sawtooth wave (I'm assuming this was FFT). Then he saved the plots as images and combined them pixel by ...
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Blind 1D equalization/deconvolution with some knowledge of filter kernel

Let $s_{\rm out}[n]$ be the 1D output signal of a system, $s[n]$ be the input, and $k[n,q]$ be the filter kernel for an element $n$ and for fixed value $q$. Then: $s_{\rm out}[n] = s[n] \ast k[n,q]$ ...
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Deconvolution of 1D Signals Blurred by Gaussian Kernel

I have convolved a random signal with a a Gaussian and added noise(poisson noise in this case) to generate a noisy signal . Now I would like to deconvolve this noisy signal to extract the original ...
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Why do linear systems show sinusoidal fidelity?

I am looking for a proof for sinusoidal fidelity. In DSP we study a lot about linear systems. Linear systems are homogenous and additive. One more condition it satisifies is that if a signal is a sine ...
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What type of circuit is responsible for convolution in the classic analog telephone?

I'm interested in learning how telephones work, so I did a little bit of reading about signal processing. When I came up with the word convolution, I quickly realized the importance of this term. To ...
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Difference between linear convolution and circular convolution for a kernel

If I understood correctly (and this page should confirm: http://www.cs.ioc.ee/~khoros2/linear/convolution-teo/front-page.html) if I convolve linearly (the usual point-to-point multiplication and ...
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Kernel convolution in frequency - weird “padding”

I don't know whether this is the right place to post this, but I suppose it is. I know that frequency multiplication = circular convolution in time space for discrete signals (vectors). I also know ...
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What is the difference between convolution and cross-correlation?

I've found on multiple sites that convolution and cross-correlation are similar (including the tag wiki for convolution), but I didn't find anywhere how they differ. What is the difference between ...
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Overlap-Add versus Overlap-Save

What differences or other criteria can be used to help decide between using overlap-add and overlap-save for filtering? Both overlap-add and overlap-save are described as algorithms for doing FFT ...
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Transpose of convolution

I have an $n \times n$ asymmetric convolution kernel, $k(t_1,t_2)$. $k$ is zero everywhere except for in small regions near the corners. I also have an $n \times n$ image, $f$. Let $*$ denote ...
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2answers
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Standard Deviation in Gaussian Blur

I have a function that performs gaussian blur on image for some specific $\sigma$ (the standard deviation). It first computes kernel of size $\lceil 3\sigma \rceil$ and then performs convolution with ...
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Deconvolution Question on Article “Deriving Intrinsic Images from Image Sequences” by Yair Weiss

there are n derivative filters: $f_i$, and denote $f_i^r$ as $f_i$'s reverse filter such that $$f_i(x,y)=f_i^r(-x, -y)$$ $r_i, f_i$ given, to find $r$ from the equations: $$f_i * r = r_i, (1 \leq i \...
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Understanding the transfer function of an FIR filter

I'm currently studying FIR filter and am having trouble understand how the following equation works, and it's implication. $$ y[n] = h[n] * z^n = H(z) \cdot z^n $$ I don't really understand how this ...
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How to remove the boundary effects arising due to zero padding in scipy/numpy fft?

I have made a python code to smoothen a given signal using the Weierstrass transform, which is basically the convolution of a normalised gaussian with a signal. The code is as follows: ...
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Help solving a convolution problem

I'm finding in trouble trying to resolve this exercise. I have to calculate the convolution of this signal: $y(t)=e^{-kt}u(t)*\frac{\sin\left(\frac{{\pi}t}{10}\right)}{({\pi}t)} $ where $u(t)$ is ...
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What are the characteristics of a “good” smoothing convolution kernel?

At work we were smoothing a signal by convolving with either f1=[0.2000 0.2000 0.2000 0.2000 0.2000] or ...
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Generate the Convolution Matrix of 2D Kernel for Convolution Shape of `same`

I want to find a convolution matrix for a certain 2D kernel $ H $. For example, for image Img of size $ m \times n $ , I want (in MATALB): ...
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How to 'interpret' the Fourier Transform (specifically, of a convolution kernel)

As part of a homework assignment, I had to take the Fourier transform of the kernel I was using to convolve a signal. The kernel was a constant rectangular function, that was 1 within the square $(-1,...
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When convolving two functions that are constants in a region and 0 everywhere else, where does the integration start?

Heads up, this is for homework. I never took a signals and systems course, so I'm behind on this stuff. I want to compute the convolution of two rectangular regions. I know the standard equation ...
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MOD-N Circular Convolution

How to find MOD-2 Circular convolution for the two sequences $h =[-1,3,-2,1]$ and $x = [1,-1,-2,1,3,2,1,2]$. I know the answer is $7$ $0$ from matlab but I don't know how to find it graphicly or ...
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2answers
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Sampling theorem and Dirac comb

I am reading "The Scientist and Engineer's Guide to Digital Signal Processing" and trying to understand Figure 3.5 below which is about the sampling theorem and aliasing. I do not understand the ...
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Is it possible to simplify the convolution integral if the functions are non-zero in disjoint areas? [duplicate]

Possible Duplicate: When convolving two functions that are constants in a region and 0 everywhere else, where does the integration start? I have a function $f(x,y)$ and $h(x,y)$. $f(x,y)$ has a ...
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1answer
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How to find the convolution kernel in frequency domain?

I have a two vectors of spatial data (each about 2000 elements in length). One is a convolved version of the other. I am trying to determine the kernel that would produce such a convolution. I know ...
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2answers
273 views

Question on 2-D Convolution

This was a question on one of my past year paper questions. Question: Prove $$f(m,n)*g(m-r,n-s) = f(m-r,n-s) *g(m,n)$$ where $f(m,n)$ and $g(m,n)$ are 2-D discrete functions, $r$ and $s$ ...