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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743 views

Convolution in spatial domain is multiplication in frequency domain

I have to prove convolution in spatial domain = multiplication in frequency domain using two matrices. $$ x(m, n) = \begin{bmatrix} 1 && 2 \\ 3 && 4 \end{bmatrix} $$ $$ h(m, n) = \...
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1answer
543 views

Linear convolution of discrete signals with defined lengths

What is the maximum count of non-zero elements, that can a linear convolution of discrete signals of "lengths" 5 and 7 have? When I label the length of signal $x[n]$ as $M$, and the length of signal $...
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1answer
236 views

Autocorrelation function

For what signal applies, that its autocorrelation function at point $0$ is zero, i.e. $R_f(0) = 0\ ?$ I know that autocorrelation is (RootMeanSquare)^2 and for $R_f(0)$ this equals: $$ R_f(0) = \frac{...
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1answer
65 views

Create an input so that poles show up as outputs?

Let's say we have a rational, causal, stable LTI system with transfer function $$H(z) = \frac{A(z)}{B(z)}$$ If $H(z)$ has $N$ poles, we can in theory have only 1 of those poles, $p_i$, show up at the ...
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1answer
350 views

Convolution between two unequal length vectors

Considering an example, where the model is \begin{align} x[n] = \mathbf{h}^\mathsf{T}\mathbf{u}[n] + w[n]. \label{Eq1} \end{align} $\mathbf{h} = [h_0,h_1,\ldots,h_{M-1}]^\mathsf{T}$ of length $M$ ...
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0answers
32 views

Where does convolution fit into tracking fluorescent photons using MC models?

I have been reading this old paper by Steven Jacques, a titan in the world of using Monte-Carlo methods for photon propagation and distributions. https://www.osapublishing.org/ao/abstract.cfm?uri=ao-...
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1answer
223 views

How to calculate multiplication of two discrete series

Short version: How to multiply two discrete sequences? Long version: Convolution of two discrete sequences is weighted sum. For instance, convolution of two sequences: ...
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2answers
122 views

why exponential term neglected in equation?

where does that exponential term gone, is this because it is a constant term or it has to do something with stablity?
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1answer
34 views

Question on LSI system

Why second option (1) is not correct ?
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1answer
82 views

Are convolution and multiplexing synonymous?

Other than preferences to use one or the other words in different domains, do they refer to essentially the same process? And likewise for the opposite operations, demultiplexing and deconvolution?
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1answer
170 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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1answer
203 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
136 views

Impulse response time period in circular convolution

While considering an input to be periodic of Period N, can the impulse response not be periodic of period greater than N ? If it can be, how can one compute it’s convolution?
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1answer
430 views

Question on convolution

I am stuck at question number 2.8 This is how I have gone about solving it: I have calculated $y(t)$ by convolving $x(t)$ with $h(t)$ using the fact that $x(t)$ convolved with an impulse at $t=t_0$ ...
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3answers
247 views

How to correct phase of Diagonal Volterra kernels obtained with exponential sweep sine?

I'm trying to model a non-linear system using non-linear convolution with Novak's (2010) synchronized exponential sine weep (SESS) that models them with a Generalized Hammerstein (Volterra diagonal). ...
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1answer
483 views

Why correlation is not associative in the context of image processing?

I can see most of the places it says "convolution is associative, while correlation, in general, is not". Denote $*$ convolution operator, let's say you have an image $f$, which you need to convolve ...
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1answer
115 views

Underdetermined deconvolution of windowed output

Consider a discrete 'blurred' output $h[t]$ given by the convolution of filter $f[t]$ and signal $g[t]$. This question considers recovering $g[t]$ from a window (subset) of $h[t]$. This causes the ...
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1answer
574 views

Identifying origin in convolution table

I am taking the convolution of $x(n)=\left\{2,1,-1,-2,3 \right\}$ with $n=0$ at the third position with $h(n)=\left\{1,2,0,3 \right\}$ with $n=0$ at the second position. The answer is $y(n)=\left\{2,5,...
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3answers
1k views

Convolution of even functions is even

Prove that the convolution of two even functions is an even function. I have my own proof which I have included as an answer, but it assumes a linear time-invariant system. I want to know if there is ...
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2answers
920 views

Circular convolution of length L of sequences of length greater than L

I'm trying to understand how may I obtain the circular convolution of length L when the sequences I'm trying to convolve are of length greater than L. For instance this Matlab code using sequences ...
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1answer
382 views

2D Convolution in MATLAB Causes Artifacts (Boundary Issues)

I`m trying to do a 2D fast convolution in Matlab of large matrices. If I use FFT version based on convolution theorem ( https://en.wikipedia.org/wiki/Convolution_theorem ), there are some artefacts in ...
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1answer
442 views

Convolution of $\sin(\omega t)$ and $\cos(\omega t)$?

If $x(t)=\sin(\frac{\pi t}{4})$ and $y(t)=\cos(\frac{\pi t}{4})$ then i need to find the Convolution $$z(t)=x(t) \circledast y(t)$$ So convolution will be $$\begin{align} z(t) &=\int_{-\infty}^{...
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0answers
146 views

Imfilter, FFT-bsed convolution speed

I want to convolve two large matrices and it is working fast - as long as one of those matrixes contains only separate points (point sources). If I replace the points by eg. Gaussians (line "HERE" ...
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3answers
1k views

Volterra Kernel Convolution Method

Here I understand that the first term is a simple convolution of the input signal with first volterra kernel that I have acquired through farina sweep method, my question is if the second term is the ...
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1answer
556 views

Find the nyquist sampling rate?

I have a signal $x(t)$ for which I want to find the Nyquist frequency : $$ x(t) = \frac{\sin{\pi t/2}}{\pi t/2} \ast \sum^\infty_{n=-\infty}\delta(t-10n)$$ I am trying to solve this in the time ...
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1answer
659 views

Circular vs Linear Convolution

When deriving DFT from DTFT,we sample the frequency domain with uniformly spaced samples,hence adding periodicity to time domain. But DFT requires a limited support: we take only 1 period. Does that ...
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1answer
1k views

Convolution in frequency domain, what is the output bandwidth

If two signals do convolution in frequency domain, would the output width/BW be related to the width/BW input signals? Would it be addition or any other?
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1answer
586 views

Downsampling and convolution

(Code snippet with example below). In MATLAB, assume I have a long signal vector y (length N) that I wish to convolve with a ...
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1answer
111 views

Apply LTI filter to incoming signal stream [duplicate]

Typically, when I want to filter a signal with an LTI filter (in this case a low-pass filter), I just convolve the signal with the filter. However, what do I do if I have a stream of data that I want ...
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1answer
473 views

Exponential decaying step response in LTI System

I'm attempting to better understand the relationship between step responses, impulse responses, and convolutions. Say that I have a system where if I apply a constant input, my output decays from a ...
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2answers
500 views

Does the impulse response of a system have any physical meaning?

In other words, what does the impulse response tell us about the characteristics of the system? For simplicity, let's assume we deconvolve a discrete output and a discrete input to obtain an impulse ...
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1answer
983 views

Why a Convolution Matrix Is Called a Kernel?

According to Wikipedia: In image processing, a kernel, convolution matrix, or mask is a small matrix. I am wondering, why the matrix is called a kernel? Does it has anything to do with kernel ...
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2answers
112 views

Question related to Deconvolution and Fourier Transform

Currently I am completely new to Signal Processing and I am about to kick off a project related to the system identification. The general idea is given a pair of sent and received signals, I have to ...
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0answers
376 views

discrete fourier transform circular symmetry

I was reading digital signal processing. In topic Discrete Fourier Transform, circular symmetry it is said that circular advance is obtained by shifting x(n) in clockwise direction. i.e. to obtain x(n+...
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1answer
46 views

Can cross-c.(x,y) be positive if signals x and y do not share frequencies?

The question is if the cross-correlation of two signals $x$ and $y$ can be non-zero even if $x$ and $y$ do not share frequencies. My approach is the following: The cross-correlation $\rho_{xy}\left(\...
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3answers
402 views

Fast way to calculate a few points in convolution?

Say I have two 1000-point sequences. I can compute the entire convolution fairly efficiently using FFTs (keeping in mind that zeroes have to be padded on to avoid doing a circular convolution). ...
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1answer
213 views

Question about correlation of two signals

I'm working on some practice examples and in one of them I'm asked to find the convolution and the correlation of some signal pairs given. I know that correlation , given two signals x(n),g(n), is ...
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1answer
347 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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1answer
731 views

How to “scale” the FFT when using it to calculate discrete convolution?

As you probably know, the discrete convolution $ H = F \ast G $ of some $ F \left[ x \right] $ and some $ G \left[ x \right] $ can be calculated using the Fast Fourier Transform (FFT). To do this, ...
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1answer
237 views

Why Filter Kernel is flipped during convolution process? [duplicate]

Why Filter Kernel is flipped during convolution process? What are the consequences if the kernel is not flipped? Note: Filter Kernel means: Impulse response or convolution kernel.
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1answer
985 views

Convolution by differentiation property of convolution

This is the question when i am trying to do it by the deravative property of convolution https://en.wikipedia.org/wiki/Convolution#Differentiation like this Actual answer should come like this $...
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1answer
66 views

Convolution Input/output Units

How come are the units of convolution for LTI system not consistent? $$y(t)= \int_{-\infty}^{\infty} x(\tau)h(t-\tau)d\tau$$ $y(t)$ unit is volt, whereas the RHS has volt.time unit!!!!
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1answer
108 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
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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3answers
483 views

Minimal number of additions in convolution

The Winnograd algorithm can be used to reduce the number of multiplications in convolution. Is there a known method of reducing the number of additions in convolution?
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1answer
513 views

PDF of a sum of two RVs by convolution of their samples via fourier transform in Excel

I apologies if this is off topic for this site, but I am trying to figure out (and not having much luck) how to get an empirical distribution function of a sum of two random variables given two ...
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0answers
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How to convert multi-band Energy Time Curve (ETC) to Impulse Response (IR)?

I am running my own sound simulator. Now I have obtained the Energy Time Curve (ETC, expressed by energy) by physical simulation, and they are stored in 8 discrete frequency bands (because decay of ...
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2answers
219 views

2D Image Convolution: Spatial Domain vs. Frequency Domain Convolution in the Computational Complexity Sense

I want to convolve 2 images I1 and I2. Let's assume they have the same size. I know 2 methods: 1) Use direct definition of 2D convolution 2) i. Computer FFT of I1 (call it I1_FFT) and FFT of I2 (call ...
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1answer
293 views

3D FFT's and Convolutions using FFTW

I am trying to perform a of convolution 2 3-dimensional vectors using the FFTW3 library in C. My question relates to the order in which the frequency domain appears and if it will make a difference ...
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5answers
561 views

Fast & accurate convolution algorithm (like FFT) for high dynamic range?

It seems that FFT-based convolution suffers from limited floating-point resolution due to evaluating everything around the roots of unity, as you can see in the $10^{14}$-factor error in this Python ...