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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51
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17answers
138k views

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?
47
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4answers
43k 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 ...
26
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6answers
15k views

Flipping the impulse response in convolution

During convolution on a signal, why do we need to flip the impulse response during the process?
24
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1answer
15k 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 ...
22
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1answer
6k 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 ...
18
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1answer
38k views

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 ...
15
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5answers
12k 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 ...
14
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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 ...
12
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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 ...
11
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12answers
31k views

Deconvolution of 1D Signals Blurred by a 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 ...
11
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4answers
16k views

How Does a Convolution Can Be Expressed as a Matrix Multiplication (Matrix Form)?

I know this question may not be very relevant to programming, but if I don't understand the theory behind image processing I'll never be able to implement something in practice. If I got it right ...
11
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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 ...
11
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2answers
22k 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 ...
10
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3answers
1k 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 ...
9
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4answers
2k 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?
9
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5answers
5k 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 ...
9
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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 ...
9
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1answer
705 views

Solving a Convolution Problem of a 1D Signal

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 ...
9
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5answers
107k 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 ...
8
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2answers
371 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 ...
8
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5answers
662 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 ...
8
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4answers
21k 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 ...
8
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2answers
4k 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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2answers
7k 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
votes
1answer
278 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 ...
7
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7answers
546 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 ...
7
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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 ...
7
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2answers
106 views

Do $|s(t)|$ and $|S(f)|$ uniquely determine $s(t)$?

Consider a signal $s(t)$. My question is if you know $|s(t)|$ and $|\mathcal{FT}[s(t)](f)| = |S(f)|$ or equivalently $|s(t)|^2$ and $|S(f)|^2$ is it possible to determine $s(t)$? That is, is $s(t)$ ...
6
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1answer
317 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) ...
6
votes
1answer
258 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 $...
6
votes
1answer
376 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 \...
5
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3answers
1k views

How do impulse response guitar amp simulators work?

I am wondering how impulse response guitar amp simulators/modelers work. I thought it was a matter of convolving a signal of recorded impulse response in time-space with a guitar sample. I tried to ...
5
votes
1answer
324 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: ...
5
votes
4answers
3k 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 ...
5
votes
4answers
745 views

Can every type of linear filter be modelled by a convolution?

I have an input time series going through a filter that creates another time series as output. If I assume in first approximation that my filter is linear, does it necessarily mean that I can model ...
5
votes
2answers
6k 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 ...
5
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3answers
5k 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 ...
5
votes
3answers
326 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, ...
5
votes
2answers
660 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 ...
5
votes
2answers
1k 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 ...
5
votes
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
votes
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 ...
5
votes
1answer
3k views

How do real-time convolution plugins process audio so quickly

Okay, so in Logic Pro I can load up a Space Designer plugin (convolution reverb) with an impulse that's 9.1 seconds long, turn my mic on, and get real-time convolution reverb as the mic records ...
5
votes
1answer
12k 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 ...
5
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3answers
5k views

An Intuitive Way to Understand the Sharpen Convolution Filter in Image Processing

Can someone explain sharpen in a non-technical way. So, I don't mean that you need to multiply every pixel with 5 and subtract it with the pixel left, under, above and right.
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
votes
1answer
4k views

Convolution Kernels for Image Filtering

As I understand it, in image processing, when it is desired to apply a filter of some sort to an 2D image, a kernel is applied to all the pixels of the 2D image in a process called convolution. Median,...
5
votes
1answer
2k views

Common Use Cases for 2D Non Separable Convolution Filters

In the image processing world, I've noticed that a lot of the popular convolution filters are separable. Here's a quick list of common separable filters: Sobel Gaussian blur Box filter (all ones, for ...
5
votes
1answer
135 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 ...
5
votes
1answer
2k views

Image Gradient - Flipping Effect of the Convolution Matrix (Kernel) for Edge Detection

Prewitt operator is a common operator to compute image gradient in edge detection, and I knew that to apply this Prewitt operator to an image is just to convolve them together, say, the image is ...