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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 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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1answer
1k views

Generate the Matrix Form of 2D Convolution Kernel

We know that a convolution can be replaced by a multiplication with a toeplitz circulant matrix. Meaning, assume I have convolution kernel $h$ and matrix $I$ (of size $m \times m$ for example), then ...
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GCC-PHAT (Generalized cross correlation) always peak at delay=0 on real audio signal

I have studied the GCC-PHAT algorithm to estimate TDOA on audio signals at 2 mics. Here is my MATLAB implementation: ...
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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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Support of the convolution of two rectangular signals

I'm trying to convolve two rectangular signals in the frequency domain $$H_1(\omega) = u[\omega +.2\pi] - u[\omega -.2\pi]$$ and $$H_2(\omega) = u[\omega +.1\pi] - u[\omega -.1\pi]$$ My result is a ...
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425 views

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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283 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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Implementing Convolution with FFTW

UPDATE I've now implemented a timeshift on both the filter and the input signal, but this does not remove the noise. The plot below shows the original mono track in the upper panel. The middle panel ...
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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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How to implement freq convolution layer?

I am referring the paper https://pdfs.semanticscholar.org/31c7/4962122ba5fe1c469101b5bc2ae6d88c9c18.pdf. In the paper, for CLDNN network first layer is freq convolution. How to implement the same for ...
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Wide-Band Lorentzian FDTD Algorithm

I want to convert a simulated gain/absorption of a material, which can be understood as a discreet (dispersive?) function $g_i(f_i)$ ($f$ is for frequency) or $g_i(\lambda_i)$, into $\tilde g(t)$ for ...
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Cannot figure out the convolution operation in this problem

A linear system S has the relationship $y[n]=\sum_k {x[k]*g[n-2k]}$, k ranging from $-\infty$ to $\infty$, between its input $x[n]$ and output $y[n]$, $g[n]=u[n]-u[n-4]$. Determine $y[n]$ when $x[n]=...
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Convolution in the Hartley Domain

The convolution Theorem of the Hartley Transform is given by $$ Y_{Ha}(k) = X_{Ha}(k)H_{Ha}^{e}(k) + X_{Ha}(-k)H_{Ha}^{o}(k) $$ where, $$ H_{Ha}^{e}(k) = \frac{H_{Ha}(k) + H_{Ha}(-k)}{2} $$ $$ H_{...
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Applying a filter on an input sequence in matlab

Given a input sequence $x = {x_1, ... x_n}$ and a filter with l elements $h = [h_1, ..., h_l]$ with l < n. We want to filter the input sequence with the specified filter. My first thought was to ...
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182 views

Question about convolution of shifted function-simple

I memorized the convolution formula, all good. I started doing examples and in one of them I had to calculate the convolution of a shifted function with another one. I know the property $$H(x)=f(x)\...
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How to simplify this sequence

So I had this question (f) at my last exam that I failed and I'm now studying for my re-exam, the problem is that I still don't know what the answer is supposed to be in this question (f): Do you ...
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Resources for learning Sound Processing [closed]

Does anyone know of any resources that explain simply, these are the data objects and variable definitions involved when doing sound processing? I took a class on image processing where we learned ...
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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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1answer
2k views

Implementing Frequency Domain Convolution in MATLAB (Convolution Theorem)

I'm trying to prove convolution in time domain is same as multiplication in frequency domain but I'm not getting the same answer in matlab. Here is the code:
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1answer
218 views

applying convolution theorem swaps quadrants

For educational purposes I implemented the DFT and inverse DFT for images using OpenCV. Applying the DFT to an image and taking the inverse DFT of the spectrum yields the original image, so this works....
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1answer
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2D Convolution as a Doubly Block Circulant Matrix Operating on a Vector

I was reading Fundamental Image Processing, Chapter 5 (Image Transforms), I encountered the following problem: Given the arrays $x_1(m,n)$ and $x_2(m,n)$ as follows: Write their convolution $x_3(m,n)...
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Convolution of signals sampled on a logarithmic grid

Is there a practical accelerated algorithm or a theoretical discrete (Fourier) transform based method to convolve discrete-time signals sampled on a logarithmic grid? What I mean is representing a ...
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Why convolution in time and frequency domain are not equal?

I was writing this Jupyter Notebook. Then, I unexpectedly faced two visually similar output, but their numerical results were very different. This is the code I used for convolution in the time ...
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1answer
88 views

Convolution of Input signal and Impulse response

I can solve the output if the input is $$ x[n] = \delta[n+1] + \delta[n] + 2\delta[n-1] + \delta[n-2]$$ and the impulse response is $$ h[n]= 3\delta[n] − 2 \delta[n−1] − \delta[n−2] + \delta[n−3]$...
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Convolution of real with complex signal

Let $x[n]$ be real signal and $y[n]=\exp(j3\pi n)$ be a complex signal Would the convolution between those two signals be $$x[n] * \Re(y[n]) + jx[n]*\Im(y[n])$$?
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How to find the impulse response of filter that outputs the autocorrelation of the input?

I am trying to solve question 9.61 in the attached image. I guess, by evaluating the autocorrelation for a specific instance, say $ t = 0 $ , that the impulse response, $h(t)$, should be : $$ h (t)...
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1answer
42 views

Explain the formula of convolution and convolution theorem

As stated in the title, I have two questions Why convolution is defined as $(f*g)(x) = \int_{-\infty}^\infty f(t) g(x - t) dt$ instead of just $\int_{-\infty}^\infty f(t) g(x + t) dt$ ? Why we need ...
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Why using the impulse respond of an LTI to characterize its output?

We all know that every LTI, is defined by its transfer function, so we can determine the output of any system, (using common transforms). It is also known that we can determine the output of any LTI ...
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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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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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How does an LTI system produce multiple values from a unit impulse

I understand that in a discreet system, an impulse is 1 at the origin point and 0 everywhere else. I've seen many examples showing the impulse response of an LTI system to be many points, have many ...
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1answer
41 views

How to increase the sharpness of the image using convolution matrix?

I am using 3 X 3 convolution matrix to obtain an sharpness image. But the output result obtain from the above matrix is not much sharpen image. How to increase the sharpness of the image ? Ya i am ...
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Principal component analysis (PCA) on convolutional network features

Please, I have a question regarding PCA and features which are extracted from a convolutional layer. link if we have a test dataset , and we extract all conv features of all images at test dataset ...
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2answers
277 views

Two real time signals convolving

This might be a stupid question but is it possible to convolve two real-time signals together? I know that generally for running convolution you have the IR and the block of the real time signal and ...
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1answer
93 views

Reduce signal size to compare them

I have multiple experiments and each of them produce several ($k$ for example) binary signals; some artificial example next: I have a metric to compare experiment results but I need vectors of equal ...
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1answer
437 views

Comparing band-pass filters and convolutional kernels?

I am currently working on extracting features for speech recognition purposes. I wanted to try an approach similar to MFCC features in which the center frequency of each band pass filters are placed ...
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Convolution with rectangular function

I have a system $h(t)=4e^{-4(t-4)}u(t-4)$ and I want to response of the system to $x(t)=rect(2(t+4))$. I have followed those steps: $y(t)=x(t){*}h(t)$ $=rect(2(t+4)){*}4e^{-4(t-4)}u(t-4)$ $=4[u(t)-...
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1answer
145 views

Filter design to realize Cauchy product

I come from Computer Science so please pardon for my possibly wrong terminology. I need to design a filter which has coefficients $$h_0, h_1, \ldots, h_n, \ldots \quad\text{such that}\quad h_0 > ...
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1answer
47 views

Wavelet transform of a spatial convolution

Does anyone know if there exist a kind of convolution theorem for the discrete wavelet transform (decimated or undecimated)? In other words can I find a simple form of $W\left[ \int f(t) g(x-t) \, ...
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2answers
736 views

Are Convolution and Deconvolution Kernels 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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1answer
118 views

Intervals of convolution product

Given are two Signals $x_1[n]$ and $x_2[n]$. $x_1[n]$ is in Intervall $[0,2]$ different than null and $x_2[n]$ is in Intervall $[0,3]$. The convolution product is Null outside intervals: $[0,6]$ and $[...
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0answers
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Noising audio in MFCC space

I am training up an audio recognition neural network using MFCCs. Its been shown to be very beneficial to artifically add noising and reverb of the original audio when training a neural network (Data ...
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1answer
148 views

Phantom harmonics when using cosine windows why do they appear and how to avoid them?

Given an L order cosine window, it is possible to show that the width of the main lobe is given by: $$\omega_w = \frac{2 \pi L}{(2N+1)}$$ Where $L$ is the order of the window, $N$ is the maximum ...
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1answer
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Upsampling signal using convolution-based interpolation filters

I am currently reading this paper which discusses several image interpolation methods, such as nearest neighbor and linear interpolation, using convolution filters. I first want to do this in 1D with ...
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1answer
364 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 \...
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2answers
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How to understand the discrete and continuous convolution in matlab?

For example,I want to calculate the convolution of two continuous signal in matlab as the image shows. Indeed, I chose to discrete the signal to compute in matlab. Obiviously, the 1st and 3rd are ...
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1answer
216 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 $...
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1answer
260 views

Filtering White Noise to Generate Harmonic Signal

I have studied convolutions and filters a long time ago. Today, I am trying to review the basics using some notes of mine, but I am finding difficult to solve easy problems. Since I don't have ...
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2answers
260 views

the sub-range of circular and linear convolution

circular convolution $x_{_3p}[n]$ = $x_1[n]~\circledast_N ~x_2[n]$ is a period version of the linear convolution $x_{_3p}[n]=x_1[n] * x_2[n]$ The length of $x_1[n]$ and $x_2[n]$ are $L$ ($n\in[0,\...
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1answer
2k views

Recursive systematic convolutional code (RSC) realization in MATLAB

How can I implement $\rm RSC(2,1,2)$ in MATLAB? Can I use convenc function to build RSC? The convenc function has 2 arguments: ...