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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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Add echo as described by difference equation to audio signal (in MATLAB) [closed]

A simple linear system is echo. It can be described by equation $$ y[n] = x[n]+ k\,x[n−d], $$ where $n$ represents sample index, $k$ represents an attenuation coefficient, and $d$ represents time lag....
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7answers
459 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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1answer
481 views

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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1answer
40 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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1answer
83 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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1answer
48 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
27 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
99 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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2answers
105 views

Why Convolution between Signal and a 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
66 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
43 views

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
68 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 ...
2
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1answer
271 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
47 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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1answer
89 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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1answer
39 views

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
209 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
92 views

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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1answer
37 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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3answers
480 views

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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1answer
123 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
356 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
126 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
112 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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1answer
412 views
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1answer
61 views

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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1answer
64 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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1answer
120 views

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
95 views

Count Matches to a 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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1answer
157 views

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 ...
3
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2answers
112 views

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
132 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
211 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
36 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
26 views

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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0answers
48 views

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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0answers
186 views

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
112 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 ...
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3answers
83 views

Difficulties while understanding Convolution [duplicate]

I have just started convolution sum. I am able to do Mathematical convolution sum. But I am unable to make a figure of it in my mind. So I tried to go through the graphical convolution. Below is the ...
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1answer
190 views

Convolution Sum [closed]

I understand convolution is linear combination of delayed impulses of decomposed signal. $$\int_{-\infty}^{+\infty} x(\tau)h(t-\tau)\mathrm{d}\tau = g(t)$$ I want to know about these decomposed ...
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1answer
1k views

Convolution and cross-correlation on 2D image (Example)

I have read that convolution and cross-correlation are the same thing, but convolution flips 180 degrees (images), or time reverses (sequences) the kernel, before performing the elementwise ...
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2answers
306 views

pdf of the sum of gaussian distributions using fft Ask [closed]

I am trying to derive the pdf of the sum of independent random variables. At first i would like to do this for a simple case: sum of gaussian random variables. I was surprised to see that i don't get ...
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1answer
244 views

Is there any relationship between the convolution and cross-correlation of two signals? [duplicate]

There are two square 2-D signals with the same size $m \times m$, if the result of convolution of those two signals is first picture, And the result of cross-correlation of those two signals is second ...
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0answers
30 views

How do I draw convolution? [duplicate]

I know what is form for convolution but when I try to draw that I never get good answer. I think I don’t understand that good. How someone explain me with picture convolution of u[n]-u[n-5] and u[n+3]-...
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2answers
127 views

Problem with convolution

For a flat fading channel (SISO system) we have: $y=h \star s+n$ But for a mimo system, we have: $y=Hx+n$ with $H \in \mathbb{C}^{N_r \times N_t}$ Why is there not the product of convolution for a ...
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2answers
331 views

Bandwidth of product of two signals

POINT 1: According to convolution theorem, if g1(t) has a bandwidth B1 and g2(t) has a bandwidth B2, then product g1(t)g2(t) has a bandwidth = B1 + B2. POINT 2: Now, consider an AM waveform s(t)=g(t)...
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1answer
293 views

1D convolution and deconvolution using FFT

The task: there is some original signal, and there is some response function. I need to convolve them using FFT and then do deconvolution to restore original signal. The task graphical illustration ( ...
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1answer
57 views

Finding the output of a system where the input is a sum of complex exponentials

So, I have to find $H\{ x(t)\})$ (which is an LTI system), where $$x(t) = \sum_{k=0}^{\infty} a_ke^{ \ jw_kt}$$ and where the impulse response of the system is given by: $$h(t) = \frac{\delta(t+\tau)-\...
2
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0answers
117 views

Gaussian filter convolution giving unexpected results

I am trying to smooth a time series signal with a Gaussian filter and then differentiate the signal (this is for an application for edge detection). A nice property of convolution is: $$ \frac{d}{dx} \...
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0answers
38 views

Recursive systematic convolutional code with TCM

My question is: What are the outputs from the TCM encoder ?