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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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How do you apply a filter after DFT on an image?

Let's say size of the image is 100 x 100 and the kernel matrix is 5x5. I took the DFT of both the image and the kernel. But how do I multiple these two matrices? And which parts involve in these ...
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add echo described by equation to audio signal (matlab)

A simple linear system is echo. It can be described by equation $$y[n] = x[n]+ k\,x[n−d]$$, where $n$ represents sample, $k$ attenuation coefficient and $d$ lag. How can I add echo to an input signal ...
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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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Associative Property of Convolution:

Consider the following sequences: $x_{1}(n) = A$ (a constant), $x_{2}(n) = u(n)$, $x_{3}(n) =\delta(n)-\delta(n-1)$. ($\circledast$ stands for linear convolution) If I perform the operation $x_{2}\...
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what does mean that sub-channel must not share common zeros

In blind channel identification, using SIMO channel or oversampling, a very common and known condition is supposed which is: "Sub-channels must not share common zeros", in other words channel must not ...
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1answer
26 views

Using Matlab's conv() function

Here is an example of convolution given: I have two questions here: Why is the vector 𝑥 padded with two 0s on each side? As, the length of kernel ℎ is 3. If 𝑥 is padded with one 0 on each side, ...
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19 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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Indexing problem with using FFT convolution to remove echo

I've been using a very basic kernel to remove a known echo from a signal via convolution in the time domain e.g assuming a signal contains a delay of 5 samples ...
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1answer
44 views

Convolution Strategy

I would like your help on a theoretical question regarding convolution. The point is to design a faster discrete-time convolution operator functioning on one-dimensional space so that y[n] = x[n] * h[...
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1answer
23 views

Equalizing a temporal sound signal with a convolution

This question is more or less the following of a previous question. The aim is to equalize some sounds signals. By equalizing, I mean increasing or decreasing some frequency ranges, a bit like an ...
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1answer
65 views

Basic confusion about the DFT and convolution

I am learning DSP (with Digital Images) and I have some elementary confusion about the convolution between two discrete periodic signals. Specifically, I have learnt that when filtering an image, we ...
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1answer
70 views

Why Convolution between signal and channel is not done directly in SIMO channel

In OFDM system, I need to transmit a signal $x$ in SIMO channel $H$ with one $Tx$ antenna and 4 $Rx$ receiver's antennas. The initial equation for that convolution is $r=Hx+n$ where $n$ is the noise. $...
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1answer
58 views

Convolution of shifted signal [closed]

If $y(t) = x(t)*h(t)$, then what is the expression for $y(t+a)$? Is it $x(t+a)*h(t+a)$ or $x(t+a)*h(t)$?
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1answer
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Equalization : using the spectral or the temporal signal?

I'm trying to equalize a sound signal - using a JAVA program - and I'm using this process : 1/ Conversion of the temporal signal to a spectral signal, using a FFT 2/ Applying a coefficient to each ...
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0answers
57 views

Eigenvalues of a product of matrices with specific structures

I'm working on a multichannel feedback system with open-loop frequency response $\mathbf{A}(\omega) = \mathbf{B}(\omega)(\mathbf{C}(\omega)-\mathbf{D}(\omega))$. The time-domain convolution matrices ...
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1answer
29 views

Prove that convolution with a separable filter is equivalent to convolution on each 1D filter

I would like to prove that convolution of an image $I \in \mathcal{M}_{m_1 \times n_1}$ with respect to a separable 2D filter $F$, (i.e., $F = F_1 F_2$, where $F \in \mathcal{M}_{m_2\times n_2}(\...
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1answer
29 views

What is the meaning of the sum of kernel components in digital image filtering?

When analyzing an image signal as a series of Dirac impulses in the continuous spatial domain, I applied continuous low pass filters (to reconstruct or smooth it) with area equal to 1 to preserve the ...
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Listener HRTF estimation algorithms

Considering that HRTF measurement is a bit complex process which requires appropriate facilities, are there nowadays algorithms or physical model based approaches that allows the prediction of a ...
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0answers
25 views

Infinite-wideness limit of Weierstrass transform (Gaussian filtering)

Weierstrass transform (Gaussian filtering), with infinitely wide Gaussian, is expected to give zero and if we start from the definition it is consistent with this expectation as $\lim_{\sigma \to \...
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1answer
44 views

Graphical method for convolution?

Is graphical method the best way to solve convolution questions whether they be discrete or continuous? I was given a question: $$x[n]=1$$ $$0\leq n \leq 4 $$ $$h[n]=\alpha^n$$ $$0\leq n \leq 6$$ ...
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Controllable Canonical Form

the transfer function of my causal filter is $G(z)=\dfrac{1}{(1+\dfrac{1}{2}z^{-1})}$, $z$ being the formal z-transform. The parameters in the controllable canonical form are therefore $a_0=1$, $a_1=0$...
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How to solve this question by using convolution?

I had previously posted this question but my method was wrong in it. Two signals are given: $$x[n]=2^nu[n]$$ $$h[n]=u[n]$$ I have to find $y[n]$. I have spent hours on this question but I am unable ...
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1answer
35 views

Comparison of Linear Convolution and N point DFT

I am studying Discrete Fourier Transform currently and I have a doubt in that. Consider two sequences {1,2,3,4} and {0,1,0,0}. When I convolve them linearly, I get this {0,1,2,3,4,0,0}. However, if I ...
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2answers
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Impulse response when input to a system is differentiated, and its applicability to find response to general inputs

I will first give a short explanation of what I am asking, and then give a more comprehensive context. If we have a LTI dynamic system acted upon by inputs $y(t)$ and producing outputs $x(t)$, , we ...
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Calculating distance to target using convolution

How can I calculate distance of some target, for example if some ultrasound radar sends pulse $A\,\text{rect}(t/T)$ and convolution of sent pulse and reflected pulse is i.e $A^2\text{tria}((t-x)/T)$.
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32 views

Convolution of discrete time signal

I'm given a discrete time signal which is as follows: $$ x[n] = \alpha^n u[n],\\$$ $$ h[n] = u[n],\\$$ Why is unit function neglected in the following step: $$ y[n] = \sum_{k=0}^{n} \alpha^{k}\\$$
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Derivation of the Optimal Matched Filter - Convolution vs. Correlation

On the Wikipedia page for Matched Filters here, there is a matrix algebra derivation for an optimal matched filter. Now, considering the output of an LTI system is found using the convolution operator,...
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Decoding for punctured convolutional encoder

I have 1/2 rate convolutional encoder which punctured to rate 3/4. The puncture pattern used is [1; 1 ;1 ;0 ;0; 1] . How to decode these punctured sequence using hard decision viterbi decoding? Can ...
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1answer
85 views

What is about the circular convolution in OFDM

In an OFDM system, serial-to-parallel conversion for data is done, then the DFT is performed and then adding the cyclic prefix (CP). My question is related to that step of adding a CP. As I know, ...
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0answers
90 views

How can I improve the Canny edge detection code?

I have converted this Matlab code for Canny edge detection into C# given that the Matlab version gives out a good output. The output from Matlab code is as follows: And my C# version's outputs are ...
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1answer
100 views

How I can perform SIMO channel convolution in MATLAB

In OFDM system, I need to transmit a signal $x$ in SIMO channel $H$ of single Tx antenna and $4$ Rx antennas. The initial equation for that convolution is $r = Hx + n$ where $n$ is the noise. As ...
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1answer
63 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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Extracting positive frequencies of discrete-time signal

Convolution in the time domain is the same as multiplication in the frequency domain. My data is sampled at 200 Hz, which means that the Nyquist frequency is 100 Hz, and all frequency content is <=...
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Seam in between output segment in linear convolution and filter design

I am attempting to design a matching filter from long sequences. I want to do this in the time domain. I have 3 inputs. Let's called it p,s, and r. The matching filter is to be designed between p and ...
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Space-time trellis coding

Can someone explain to me how to calculate the branch metric of a Viterbi algorithm for a MIMO communications system? In an example, I came across they vaguely show the calculations and I have no ...
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1answer
41 views

FIR filter design and implementation meaning [closed]

What is the output of the convolution meaning which is used in the FIR filter? how can conclude the output of the FIR filter in the output according to the input $x[n]$?
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Convolution Filter Size

I am reading a paper on dilated convolutions, and I have come across this piece of mathematics. It makes sense for the most part, except when the author says that the filter size is $(2r + 1)^2$. ...
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1answer
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Convolution offset and factor in frequency domain

See this link. The following Convolution in Spatial domain code is written in C#. ...
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1answer
89 views

Count matches to kernel

So, I have this problem where I want to apply a kernel to an image and count the number of matches that happened. So for example, if I have the kernel: $$\begin{bmatrix} 1 & 2 & 1\\ 1 & ...
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Matrix cross correlation in python

I'm currently performing matrix cross correlation in python using : C = scipy.signal.correlate2d(A,A) where A is a 2D matrix, typically a picture. As you can ...
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2answers
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What is the relation between kernel functions, kernels used in convolution and null spaces of a matrix?

I have recently started learning about machine learning and have come across kernels and null spaces. I understand that null space is the set of all vectors that satisfy the equation A.v = 0 (Where A ...
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1answer
46 views

Correlation peformed by convolution

Background: The question here is related to images in particular and not signal/waveforms. I have been reading a lot of answers about the difference between convolution and correlation but I am stuck ...
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3answers
99 views

Deconvolution Using Complex Division in The Frequency Domain

Consider these two signals: a = [1 1 0 0 0 0 0 0] b = [1 0 1 0 0 0 0 0] their convolution is c = a * b = [1 1 1 1 0 0 0 0] ...
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1answer
30 views

Numerical error while implementing a periodic pulse signal

I'm trying to illustrate the principle of constructing a periodic signal using an elementary pattern. This is the code I use (python 2.7 + numpy + scipy.signal) : ...
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0answers
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Applying BCJR equalization for LDPC encoded information

I want to apply BCJR decoder for LDPC encoded information. How can I change the BCJR originally for convolutional codes for this purpose?
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Convolution - change of variables

I am struggling trying to understand the 3rd line of the expression below. The second line can be simply visualized by letting the kernel size be 3 and $i=2$ for eg. Then $ y_2 = \sum_a x_{2+a-1}...
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extracting a room response [duplicate]

So I have a wav file containing a record of a sine sweep played on my pc and recorded by a mic. And I want to extract the room impulse of it, I've looked online but I couldn't find any clear answers. ...
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Circular Convolution, modulo N smaller than Length

I am having a small Problem here, which I can't figure out on my own. I am supposed to perform a circular convolution y[n] with three different modulo N values N =...
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1answer
63 views

Gaussian Equivalent of Convolving an Image 50 Times with a Box Filter

I have a image that I'm convolving 50 times with a box filter, and I like to replace this with a single gaussian filter. Because both box filter and gaussian filter are separable I can just study the ...