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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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Approximate Numerical Convolution with a Singularity in the kernel

I am trying to perform a numerical convolution where one of the operands is singular at t = 0. Concretely: $\int_{0}^{t}G(t-\tau)\dot{\epsilon}(\tau)d\tau$, where $\dot{\epsilon}(\tau)$ can be ...
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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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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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56 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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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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62 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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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
36 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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38 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
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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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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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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82 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
28 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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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
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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
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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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90 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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190 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
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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
75 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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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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Generating synthetic zero offset seismic data

Essentially, I am struggling with producing the depth model for this problem, which is a finite reflector dipping at an angle in the subsurface. I just started using matlab so I am not quite sure what ...
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106 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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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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Create colour-coding filter for Fourier transformations

I have to conduct a Fourier transform on a 2D-RGB-image, filter out low frequencies and then apply a colour-coding filter so that the remaining frequency peaks are represented by different colours. I ...
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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
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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)-\...
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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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Recursive systematic convolutional code with TCM

My question is: What are the outputs from the TCM encoder ?
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1answer
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Using the flip-and-drag method to draw a convolution

So, we are asked to graphically convolve (using the flip-and-drag method) the following pair of signals: $$x_1(t) = \delta(t+1)-2\delta(t-1) \ \ \ \ \ \ \ \ \ \ \ \ \ x_2(t) = \begin{cases} -1-2t, &...
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How to calculate time of arrival using room impulse response

I need to find the timestamp of arrival of a particular signal at a receiver location within a room. The known parameters are the room impulse response h for a ...
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Matrix used for a transposed convolution?

I was wondering what would be the matrix used for a transposed convolution? I understand that the matrix for Conv2d given the initialization below: ...
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Amplitude is affected by the sampling interval in convolution of input signal with impulse response?

I simulated convolution using an application, I then wanted to see if the output would match the derived mathematical output. The square wave below is being convoluted with itself, the impulse ...
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1answer
297 views

Proof of the convolution property of Fourier Series in continuous time

I am facing problem in understanding the proof of Convolution property of Fourier Series (FS) in continuous time CT; that is: $$\mathrm{FS} \big\{x_1(t)\star x_2(t)\big\}=T\sum_{n=-\infty}^{\infty}...
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1answer
38 views

Clarification on Discrete-time convolution and signal shifting

What are $y_1[n]=x_1[n]*h[n]$ and $y_2[n]=x_2[n]*h[n]$? $$x_1[n]=(0.1)^nu[n],\quad x_2[n]=(0.2)^n,\quad h[n]=(0.3)^nu[n]$$ I am confused about how to calculate $y_{1}[n]$. The formula for discrete ...
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Does Function to Function Multiplication and Convolution, Follow Laws of Convolution

Apologies this is long – I do not want to leave any ambiguity. I have a hopefully simple question, that does not seem to be covered by the DSP books I have in regards to theory of operation. I ...
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Zero Padding FFT: ifft(fft(x)) is unequal to x

I implemented an iterative radix-4 FFT and IFFT, and after performing these on zero padded, but further unchanged signal, the output differs. What am i getting wrong? Problem Description: A signal ...
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Multistage-Multirate-Filters, convolution of all impulse responses to estimate frequency response

I want to evaluate the frequency response of a cascade of filters. The Cascade is as follows: ->CIC_Deci(N1)->CIC_Deci(N2)->FIR->CIC_Inter(2*N2)-> As you see I have different decimation factors <...