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

Does anyone know how to write arg min code in matlab with explanation? I am referring to a paper for my research. I am not sure whether I can paste the paper link here. At first, I try to do feature ...
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What kind of discrete convolution is this?

Let x[n] and y[n] be defined for n=0,1, ..., N-1. This (for example with Python's scipy fft ...
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Convolution for non-signal-processing background

I am a civil engineer and am analyzing traffic data recorded by capturing vehicle movements over a highway for a specified time period. The database I am dealing with contains observations at every 0....
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Fourier Transform & Convolution to get response - confused

in the past couple of years I've always been using Laplace transform for system responses, but today tried to do it with Fourier transform and failed. What am I doing wrong? If we have a signal $x(t) ...
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What is spatial correlation and spatial convolution?

What does the term spatial correlation and spatial convolution mean with respect to digital image processing ?
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Convolving time reversed discrete input with time reversed discrete impulse response

Question 3.1 d from Chapter 3 of Oppenheim's Signals & Systems I have $$x[n]=(-1)^n{u[-n]-u[-n-8]}$$ $$h[n]=u[n]-u[n-8]$$ and the question asks for $y[n]$ which is the convolution of $x[n]$ and ...
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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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Convolution that results in an all-zero sequence

I am asked to find a pair of sequences, each one of which contains three distinct values and where the convolution is an all-zero sequence. I've came to the conclusion that one of the sequences must ...
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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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Find output of digital filter given input and transfer function?

Hey guys so I have an input sequence that are real values that represent intensity of a column of an image. I also have the transfer function in the Z domain of a 2nd order high pass filter. I have ...
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Using Fast Convolution to apply HRIR to soundwave

I have a dozen source sound waves; each is about one second duration. I want to put each one through a digital filter (I'm truncating it to 128 taps). Currently I'm doing this with a bog standard ...
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Can two nonzero signals $x[n]$ and $y[n]$ give a zero convolution

Suppose $x[n]$ and $y[n]$ are two nonzero signals(i.e., $x[n] \neq 0$ for at least one value of n and similarly for $y[n]$).Can the convolution between $x[n]$ and $y[n]$ result in an identically zero ...
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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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Determining linearity, causality, memory, and time invariability from a picture of the signal

So, this is a picture of saccadic eye movement reflected by an EOG. How can I determine if the eye movement system is linear, causal, memoryless, and time invariant from this displayed waveform? ...
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Is it meaningful to find linear convolution of just two random sequences? [closed]

Could it bring any meaning? Is this kind of convolution be useful is solving anything?
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Basic Convolution Reverb Question

I'm surveying for feasibility techniques for a potential future project that's rather out of my past areas of expertise, and I have a fairly basic question. Of course if it looks feasible I will have ...
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Mathematical proof of relationship between derivative and convolution

What I'm looking for is the mathematical proof of why we can calculate derivatives as a simple convolution of a mask, and how do we get that mask? I know it has something to do with how the derivative ...
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Savitzky-Golay Filter Coefficients and Wikipedia

I am trying to implement a Savitzky-Golay filter by following this Wikipedia page and in the first instance I have written the following Octave software code to create the convolution coefficients <...
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Simplification of a convolution-like expression

I am trying to further reduce the following expression (if there's a nicer way to write it): $\sum_{k=-\infty}^{+\infty}\sum_{p=-\infty}^{+\infty} \sum_{l=-\infty}^{+\infty} w(k) \varphi_\mathrm{y}(l-...
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Need help understanding convolution indexing

Ok, this is leaving me increasingly frustrated. This builds on a previous question here but I am still not getting the indexing, although I learned from that question all the same. Case 1: First ...
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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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Deconvolution of non-stationary, 1-D signal?

I have a time series that has been measured after convolution with a moving average filter. Knowing the parameters of the moving average filter, is it possible to reconstruct/constrain the values of ...
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Need a fast algorithm of adaptive convolution

I have to apply some kind of adaptive filter to my function $f(x).$ I present each point of my signal as a Gaussian, whose bandwidth depends on its location (not the point of observation $\textbf{x}$) ...
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Exponential average with time constant of slow, fast and impulse

I have been studying about exponential average. There are enough explanations about this at Internet, but they do not explain about the time constant. I have one channel with a $T$ seconds time ...
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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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Why use a gaussian low pass filter, when we can convolve with gaussian kernel

Sorry if this question is too simplistic, but I am new to image processing and after successfully writing two programs, a convolution program and a low pass filtering program, I noticed that for ...
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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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low pass filter after fft in matlab

I'm new to signal processing and I'm learning on my own. Therefore I might ask questions not worthwhile your time. At the moment I'm trying to figure out the concept of a lowpass filter. Using matlab ...
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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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Convolution Based Image Interpolation

From a book, I learned that image interpolation (or upsampling) can be written as a convolution like this: $$g(i,j) = \sum_{(x,y)}f(x,y)h(i-rx,j-ry)$$ while $r$ is the upsampling rate. But I have a ...
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Circular Convolution in Scilab [closed]

I am quite familiar with signal processing using Matlab. Now I am working in its open source alternative 'Scilab.' In Matlab, cconv() function is used to perform circular convolution between two ...
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534 views

Calculating sum of a discrete signal

I have to find a convolution of two signals $h[n] = 0.5^nu[n]$ $x[n] = u[n]-u[n-3]$ the final sum, which is correct is: $$\sum_{m=n-2}^n 0.5^mu[m] $$ note that i replaced n-k with m, that is $ m =...
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BER calculation in DS-UWB system

I need to calculate BER (bit error rate) for a system using spreading spectrum DS over ultra wideband (UWB). Modulation is bpsk. The spreading sequence lengths are not equal for all users. Receiver is ...
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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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Why is image blurring called convolution and not cross correlation?

I've always thought that image convolution is a weighted sum of the nearby pixels using the convolution kernel as weights. But from the description on Wikipedia, this is what cross correlation does. ...
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Why unit impulse function is used to find impulse response of an LTI system?

Hello i am working in digital image restoration field, recently i have studied concept of convolution, i studied that to find the impulse response/point-spread function of an LTI system, an unit ...
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Using DFT Circular convolution property

I am trying to make proper use of the circular convolution property of DFT. I was taught that the DFT of x[n]*CircularConv*y[n], would be equal the product of the ...
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Deconvolution of Images - How To?

I'd like to do a deconvolution of image. For example for convolution I'm using a $3\times 3$ mask with all elements $= 1$: $$\begin{bmatrix}1 & 1 & 1 \\ 1 & 1 & 1 \\ 1 & 1 & 1\...
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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 ...
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can i decompose image deblurring model?

i am working in digital image restoration field, recently i have studied image degradation model which is like that. g(x,y) = h(x,y)*f(x,y) + n(x,y) where g(x,y) is the degraded image f(x,y) is ...
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z-space replaces multiplication with convolution and frequency eigenvectors

The frequency domain is allegedly preferred because it replaces convolution of complexity $n^2$ with a diagonal matrix multiplication. Yet, I see that in z-domain we have multiplication of polynomials,...
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How to express linear convolution using positive frequencies from channel and symbol DFT vectors?

Sorry for the long question, but I'm struggling to implement something related to this question. Your help would be appreciated. Background Notation: In the sequel, the uppercase letters represent ...
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CDMA : Calculating M from m1 * w1, m2*w2, etc M as Walsh Code, M as Orthogonal COde

I have these values, m2 = 1 -1 -1 1 w2 =-1 -1 1 1 -1 -1 1 1 -1 -1 1 1 -1 -1 1 1 Im about to multiply m2 with w2 Should i multiply m2 with all of w2 (1 * -1 -1 1 1 -1 -1 1 1 -1 -1 1 1 ...
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The Effect of a Kernel on an Image By Filtering

I am going through an old exam paper and trying to understand this question where they ask us to tell them what effect the following image filter would have if its convolved with an image: ...
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A better explaination for 'there's no flipping of the impulse response' [closed]

I showed the question about flipping the impulse response to some math teachers and electrical engineers at an university. They read Dilip's answer and thought that it was hard to understand what ...
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Image processing, recognizing a small feature in a larger image

I am trying to write an image processing program to recognize bubbles in oil. It has been suggested I try computing the convolution of the image and an image of a typical bubble. i.e. : ifft(fft(a)....
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When should the sum of all elements of a gaussian kernel be zero?

I found an approximation of a 5x5 2D convolution kernel like this : Here, the sum of the elements is zero and this one was used for Laplacian of Gaussian! Another one here : This one has all ...
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How to show that this filter is a HP filter

i got a system with transfer function given by: $$H(\omega)=1-e^{-j\omega}$$ I already plot it, and that seems to be a periodic function with $H(0)=0$, $H(\pi)=2$, , is that enough to show that this ...
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Where does convolution fit in DFT?

I am trying to understand where does the convolution fit in Discrete Fourier Transform. I know that convolution is producing a third signal from two other signals. I also know that DFT transforms one ...
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Filtering $ n \times n $ Images by Separable $ m \times m $ Filters. Computation Time for Filtering Using FFT, 2D Convolution and Two 1D Convolutions

Consider filtering square $n\times n$ images by square, separable $m\times m$ filters. Give general equations for the computation time for the following approaches to this: Filtering using FFT 2-D ...