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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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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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4answers
41k views

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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6answers
13k views

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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1answer
14k views

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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1answer
5k views

How to circularly shift a signal by a fraction of a sample?

The shift theorem says: Multiplying $x_n$ by a linear phase $e^{\frac{2\pi i}{N}n m}$ for some integer m corresponds to a circular shift of the output $X_k$: $X_k$ is replaced by $X_{k-m}$, where ...
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1answer
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Difference between correlation and convolution on an image?

Could you please clearly explain what is the difference between correlation and convolution that is done by a filter on an image? I mean in terms of signal processing definition I know that ...
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5answers
11k views

What are the problems with designing an FIR filter using FFT?

I'm trying to get an understanding of the relationship between an FIR filter designed from "first principles" using a filter kernel with convolution, and a filter designed in one of two ways using FFT ...
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3answers
4k views

Why convolution is required, or what is the philosophy behind convolution?

I am working in digital image restoration field. I have read all things about convolution, that, for an LTI system, if we know its impulse response, then we can find its output by just using ...
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1answer
1k views

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
21k views

Apply a Gabor filter to an input image

I tried to apply a Gabor filter with a specific scale (according to my values of lambda and sigma, so it is (7x7) and for 4 orientations (0, $\frac{\pi}{4}$, $\frac{\pi}{2}$ and $\frac{3\pi}{4}$) to a ...
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3answers
982 views

DFT - Removing window effect in spectral domain with convolution

I was thinking about the DFT windowing subject and a thought came to my mind. A DFT will yield the spectrum of a signal convoluted with spectrum of the window used, therefore having a main lobes and ...
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2answers
3k views

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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10answers
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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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4answers
1k views

Why LTI system cannot generate any new frequencies?

Why $Y (\omega) = X(\omega)H(\omega)$ implies that an LTI system cannot generate any new frequencies? Why if a system generates new frequencies, then it is not LTI?
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5answers
4k views

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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2answers
10k views

What is the difference between Difference of Gaussian, Laplace of Gaussian, and Mexican Hat wavelet?

There are three techniques used in CV that seem very similar to each other, but with subtle differences: Laplacian of Gaussian: $\nabla^2\left[g(x,y,t)\ast f(x,y)\right]$ Difference of Gaussians: $ \...
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1answer
6k views

Auto Correlation vs Cross Correlation vs Convolution and their applications

I know from wikipedia that auto correlation in done on the same signal while cross correlation is done on different signals.But what does this actually imply in terms of application.I can always apply ...
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1answer
611 views

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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5answers
94k views

What Are Linear and Circular Convolution?

I have some basic understanding of signals and convolution. As far as I know it shows the similarities of two signals. Could I get some explanation in plain English of: what are the linear and ...
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2answers
124 views

For complex values, why use complex conjugate in convolution?

Taken from Adaptive Filter Theory (2014) written by Haykin page 110 : $$y(n) = \sum_{k=0}^{\infty} w_k^*u(n-k), \quad n=0,1,2,...$$ where $u$ and $w$ are complex values. My question is why use ...
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5answers
466 views

Fast & accurate convolution algorithm (like FFT) for high dynamic range?

It seems that FFT-based convolution suffers from limited floating-point resolution due to evaluating everything around the roots of unity, as you can see in the $10^{14}$-factor error in this Python ...
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2answers
6k views

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 ...
7
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1answer
277 views

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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2answers
3k views

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): ...
7
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1answer
307 views

How to derive $r(t) = c(t) \circledast \frac{1}{2} h_b(t, \tau)$?

Consider a linear time-variant channel. The transmitted signal is $x(t)$, the channel impulse response is $h(t, \tau)$, and the received signal is $y(t)$. Then $$ y(t) = \int_{-\infty}^\infty x(\tau) ...
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2answers
912 views

Question about convolution in time and frequency domain

My question is about the number of data points when doing a convolution (or correlation) in the the time or frequency domain. let's say we have two signals, $a(t)$ and $b(t)$ each of length $16$. When ...
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7answers
457 views

Intuition behind commutativity of convolution in LTI systems

Why is convolution commutative, as it seems to treat two signals in a different way in an LTI system? If you imagine $y[n] = x[n] \star h[n]$ with $x[n]$ being an input signal and $h[n]$ being the ...
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2answers
3k views

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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4answers
17k views

Why is circular convolution used in DSP? Why not linear convolution?

Why are we using circular convolution in DSP? What's the main solid reason for the use of it in digital processing? Why does the concept of circular convolution come more often than linear ...
6
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1answer
224 views

Analytical expression for convolution of two 2D DFTs

I am trying to do an image analysis problem on some images, and I want to calculate some things in the frequency domain which are giving me problems. Say I have an (discrete) image $I(x,y)$ of size $...
5
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1answer
286 views

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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2answers
5k views

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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3answers
4k views

Conceptually, how does real time convolution reverb work?

I've got an impulse response of a hall, it's 10 seconds long. Now say I want to apply this reverb to a wav file of some singing. I would perform a convolution of the data in two wav files and that ...
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3answers
228 views

Deconvolution of Synthetic 1D Signals - How To?

I convolved a square wave with a Gaussian wave using linear convolution. Can I get the original square wave back by deconvolving my output with the Gaussian function? I took the FFT of both signals, ...
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2answers
724 views

Why does reversing the order of these two transfer functions give me different outputs?

Consider these two systems: \begin{align} &u\ {\longrightarrow}\boxed{s}{\longrightarrow}{\boxed{\frac 1s}}{\longrightarrow}\ y\\ &u\ {\longrightarrow}\boxed{\frac 1s}{\longrightarrow}{\boxed{...
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2answers
640 views

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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1answer
5k views

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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1answer
11k views

How are two signals multiplied? And how is it different from convolving two signals?

Suppose that I have two signals $x[n] = \left\{2,4,1\right\}$ and $p[n] = \left\{5,1,8\right\}$ and I want to multiply them. How do you do that? How different is it from convolving two signals? I ...
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2answers
3k views

Simulating analog filter using convolution or converting with fft

My task is simple; I want to simulate analog low-pass filtering of an input signal, using Python. Note that the input signal is an array of values, not an analytical function. My first question is if ...
5
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1answer
3k views

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 ...
5
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1answer
119 views

Is sampling a Fourier transformed signal and fourier transforming a sampled signal the same?

I'm having a hard time understanding an assignment that states: Draw the complex spectrum of the sampled signal $f(t)$ (periodic and continuous). Do this, by first calculating the Fourier ...
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2answers
4k views

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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2answers
2k views

Implementing Convolution in Frequency Domain?

Suppose, we have a bitmap image represented as a 2D integer array, int [,] image2D; whose FFT is Complex[,] fftImage2D; ...
5
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1answer
188 views

Difference between convolving before/after discretizing LTI systems

Suppose I have transfer functions for two continuous causal linear-time invariant (LTI) systems: $F_1(s)$ and $F_2(s)$. Let $D\left\{\cdot\right\}$ denote the function that maps a transfer function ...
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2answers
139 views

How do you deconvolve irregularly sampled points?

$f:\mathbb{R}^n\rightarrow\mathbb{R}$ is a signal and $g:\mathbb{R}^n\rightarrow\mathbb{R}$ is a known point-spread function (say, a Gaussian). A system samples $f\star g$ at a known sequence of ...
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2answers
407 views

Does the impulse response of a system have any physical meaning?

In other words, what does the impulse response tell us about the characteristics of the system? For simplicity, let's assume we deconvolve a discrete output and a discrete input to obtain an impulse ...
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2answers
601 views

Using Convolution as Feature Extraction

I am now studying image processing in my spare time. My understanding of convolution is about 'response to a specific filter': When we have a raw image, or raw signal; and a filter, aka kernel; we ...
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1answer
3k views

Translation invariance in max-pooling and cascading with convolutional layer

I am reading through this page about convolutional neural networks and I am confused about the part about max-pooling (downsampling a signal/image with the maximum value in a block). Apparently, one ...
5
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1answer
910 views

Convolution of Two Kernels [OpenCV]

I've been completely stuck on a portion of my assignment for a few days now. After plenty of searching around, I have been unsuccessful in discovering information that leads me to the correct solution....
5
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1answer
367 views

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 \...