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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Time reversal of input signals in convolution

Let f(t) and g(t) be signals. I can't figure out what happens to the convolution of f(t) and g(t) if both f(t) and g(t) are reversed one of f(t) and g(t) is reversed I tried the change of variable ...
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2D FFT Toeplitz Matrix Indexing

I have a convolution sum_j M(x_i-x_j) v(x_j) which I would like to numerically compute using a FFT. x_i and ...
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26 views

Discrete-time convolution response on matlab using for loop

An LTI system's Unit impulse response is defined as: > n = 1:100; h = 0.08*(0.9).^n; if we give input signal as: ...
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Convolution Theorem using DCT

I am trying to digest this paper. [2002] Anna Usakova. Using Of Discrete Orthogonal Transforms For Convolution So far, I've been successful with DFT and DHT. Could someone give a hand with DCT? I ...
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Convolution of two rectangular pulses intuition

From what I understand the convolution of the impulse response of a system with the input to that system gives the output. Now if the impulse response is a rectangular function and the input is also ...
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Convolution introduces NaNs

I am performing convolution in MATLAB using the built in conv function. I am convolving an impulse response (length 500 samples) with an 1800 sample long input ...
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Division in the Fourier Domain (Deconvolution) - How to Handle Lengths of the Signals

In order to avoid circular convolution $y(t)$ of two functions say $u(t)$ and $v(t)$ in Fourier transforms, the data length must be at least ($u(t)$)+length($v(t)$)$-$1. If we are interested in ...
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2answers
107 views

Show Equivalence Between Multiplication in Time Domain to Convolution in Frequency Domain

My goal is to compute the Fourier of the product between two discrete time signals, y1 and y2. This can be done by computing the convolution between the fourier transform of y1, f1 and the fourier ...
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1answer
36 views

Is zero-padding necessary for speech processing to satisfy linear convolution property?

In the FFT domain, for example, if I multiply a noise reduction gain to the noisy signal, $ Y(w)H(w) $, this translates to a circular convolution in the time domain of the same length $ y(t) \...
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2answers
102 views

Image Processing on Raspberry Pi

What are my options for Open Sourced Image Processing functionality on a Raspberry Pi? So, I am referring to the old-school processing, using operators like open/close/erosion/dilation/threshold/...
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Solving nonlinear Fourier relation

I'm trying to solve the following nonlinear cross-correlation problem for the time-domain signal $f(t)$: $S(\omega) = \overline{\mathcal{F}\left[f(t)\right]} \mathcal{F}\left[f^n(t)\right]$ with $n&...
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MATLAB- Add Envelope to Sound Signal

I’m in the process of making a convolution reverb and I’m trying to add an envelope to my impulse response signal and plot it in order to change the RT60 of my sound signal (Just a song). I’ve looked ...
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Convolution in time frequency domain

I have a rectangular matrix S which is the amplitude of S-transform and a matrix G whose arrays are zero and one. G and S have the same size. Each row corresponds to time ti and each column to ...
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Convolution v.s. Cross Correlation in Digital Image Processing

I understand that from mathematical point of view, only difference between Convolution and Cross Correlation is that Convolution is commutative, while Cross Correlation is not. In many articles ...
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56 views

Best approach for discarding the ends of convolution in FT

In a recent discussion Linear vs. Circular Convolution on avoiding circular convolution by FFT, it was shown that the FFT length for convolution purposes set should be = (data set 1)+ (data set 2) -1. ...
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153 views

Linear and Circular Convolution in Fourier Domain (DFT)

Suppose we have two vectors A and B of length 100 and 80 obtained as a function of time. If we wish to perform convolution of the two vectors in the Fourier domain, we need to multiply the Fourier ...
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2answers
87 views

Smoothing in frequency domain and impulse reponse of the filter in time-domain

I have a low-pass signal in frequency domain, $$\left[f_{min}=0, f_{max}=20\,\mathrm{GHz}\right]_{n=100}$$ After re-configuring the input signal as $$X=\left[-f_{max},\ \dots\ -f_{min},\ \mathrm{DC},...
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86 views

Disagreement between Analytic Convolution and FFT Convolution

I've been working on a small project, and as a part of this I need a function that can compute the structure function of the input data. In the process of writing this part/testing it I found the ...
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33 views

How to simplify multiple addition and convolution operations into one convolution kernel

I need to perform such a conversion to simplify my image processing problem (sharpening, in green are the knowns, in red the unknowns): \begin{align} y(n,m) &= \color{green}{x(n,m)} * \left[ \...
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30 views

How do wavelet levels depend on one another?

I am working with wavelets for my thesis, and I would like to know if there is an intuitive dependency between the levels of a DWT. To make it clear: The DWT performs a convolution, and then the ...
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1answer
43 views

Output length of an IIR Filter

In general, the output length of an FIR filter is given by (N+M-1) samples, where N stands for signal length and M stands for the number of filter coefficients. Can the same formulae be applied for ...
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4answers
144 views

why only impulse signal for convolution?

Why do we only use impulse response for convolution for getting output of LTI systems. why we don't use unit step or any other signal for this purpose?
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FIR Filter implementation without padding

Is it possible to implement FIR filtering action without padding the input and coefficients? i.e. Let's say if the input and filter coefficients are of size 4, then the output will be 7 samples. So, ...
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Does Circular Convolution Correspond to Periodically Expanded Linear Convolution?

I have a question whether circular convolution and periodically expanded linear convolution corresponds in following case or why it does not? Think about a signal $x[t]$ and a signal $y[t]$ both of ...
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52 views

FIR Filter implementation vs Linear convolution implementation

I came across a C code for the FIR filter on one of the websites. It is as follows ...
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155 views

convolution vs correlation? [duplicate]

What is difference between convolution and correlation?In simple words or in a nut shell? As far as i am able to study is that Convolution is a mathematical operation used to express the relation ...
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3answers
144 views

Estimating the Signal by Deconvolution with a Prior on the Filter Coefficients and the Signal Samples

Assume I have signal $y[n]$ which is a result of convolution between channel $h[n]$ and signal $x[n]$. which means: $$y[n] = h[n] \ast x[n]$$ where $\ast$ is the convolution operation The signal $...
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71 views

Confusions regarding convolution?

As far as i have studied and understood, convolution is the process by which we can get/determine output of LTI systems While reading one web link about convolution, i came across certain notation ,...
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64 views

Sample time in convolution

I have a signal sampled at a period of 0.01 and a channel impulse response sampled at 0.1250. I convolved the signal with the channel impulse response. It is right to perform the convolution between ...
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1answer
42 views

Deep Learning: Classification vs. Convolution for Signal Restoration

Assume we have vector $X = [x_1, x_2, x_3, x_4 ,..... x_N], ∈ -1,1$. Therefore the value of $x$ is either 1 or -1. The vector $X$ is convoluted with random generated vector $Y$ whose length is the ...
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What are three different techniques to convolve a signal [closed]

I have studied convolution in time domain and frequency domain. But doesn't know the 3rd method and technique
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34 views

Is there a process for deriving special cases of convolution?

For my signals and systems homework, I was met with the following problem: Consider a CT system with impulse response given by $$h(t) = e^{-|t|}$$ and a step input $x(t) = u(t)$. Using the ...
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35 views

Can the (point-wise) multiplication of two discrete band-limited functions be inherently aliased?

I'm not fully used to the language of DSP, so forgive me if I confuse some of the notation, or if the below is trivial. I'm interested in the case where we want to do the point-wise multiplication ...
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45 views

Frequency domain multiplication

I am confused why zero-padding in the frequency domain does not result in linear convolution in the time-domain using the relationship: $$corr(a,b) = ifft(fft(a) fft(b))$$ See my process below for ...
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50 views

Proving linearity and time-invariance

This question was asked in one of our quiz. Question is Determine if the system with the input-output relationship given by $$y(t) = \int_{t-10}^{t} \cos(\tau)x(\tau)d\tau$$ is linear ...
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68 views

Basic Understanding of Convolution Operation

I would really appreciate any help in understanding this. If $$y[n] = x[n]*r[n]\tag{1}$$ then what is $y[n-n_0]$ for any system? Is it $$y[n-n_0] = x[n-n_0]*r[n-n_0]\tag{2}$$ or $$y[n-n_0] = x[n-...
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1answer
198 views

Power Spectral Density (PSD) from autocorrelation

I have a 1D fractional Brownian motion (fBm) signal, $u(x)$, of size $N$, generated through a random number generator with a gaussian mean, $\mu=0$, and standard deviation, $\sigma=\sqrt{N}$. I want ...
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32 views

Time response of complex frequency response function

In the frequency domain I have the following function: $$ H(f)=A(f)\cdot e^{i\beta(f)} $$ Where both $A(f)$ and $\beta(f)$ are known functions. The thing I would like to do is to model the response ...
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60 views

How do I pick an optimal window size for overlap add/save method algorithmically

Currently I've implemented an overlap-add method using resources on the internet, but I couldn't find a well documented way to minimize the cost of the method. In other words, how do I pick the window ...
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28 views

Wireless Channel Multiplicative Model

Let's assume a SISO channel in the equivalent baseband, the standard channel model (discrete) is: \begin{align} y(k) = h(k)x(k) + z(k) \tag1 \end{align} Where $y(k)$ is the detected signal, $h(k)$ ...
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44 views

Step-by-Step calculation of stationary wavelet transform gives shifted results?

Good morning, I am doing an SWT by hand to understand it better, and have a couple of questions. Maybe someone here has experience with this? I am using the book "Conceptual Wavelets" by Fugal, ...
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Find the output for the input $ e^{-t}u(t) $ and impulse response $ \sin 3t u(t) $

Find the convolution between $ e^{-t}u(t) $ and $ \sin 3t u(t) $. I have tried to solve it the following way. Please help me find the correct solution Solution:
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Find the convolution between $ e^{-t} u(t)$ and the gate pulse shown in the figure

Find the convolution between $ e^{-t} u(t)$ and the gate pulse shown in the figure. I have tried to solve it in the following manner. My answer does not match with the one given in the textbook. I am ...
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1answer
65 views

Zero padding in frequency domain, any tricks to speedup?

there are many situations when one has to carry some operations on spectra, like splitting a spectrum Z wide in two Z/2 spectra, or vice versa merging two Z sized spectra in a 2Z sized one. The only ...
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1answer
91 views

How to manually implement convolution with FFTs?

I'm trying to manually implement a convolution using FFTs and it isn't working as expected. I know I'm probably missing some subtlety with padding, shifting, or conjugation, (all of which I've tried ...
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37 views

convolution expression h(n,k) = h(n-k)

As a new to DSP concepts want to understand the meaning of impulse response and why we do $h(n-k)$ in convolution and $h(n+k)$ in correlation.
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44 views

How to perform dechirping of SAR image in MATLAB?

I have the transmitted pulse and the raw SAR image before range compression (dechirping). I understand the pulse compression its a convolution along the columns but I am not able to make it work. I've ...
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76 views

Synthetic Aperture Radar (SAR). How to do Range Compression?

I am trying to perform range compression to a raw SAR image [fast times, sensor position], Dr in code. I have the transmitted signal (chirp), g in code, and literature says range compression is ...
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U-nets : how exaclty is upsampling performed

In U-nets I would like a more straight-forward/detailed explanation in how the upsampling part ("right part of the U") is performed. I read that it can be done by "transposed convolution layers" aka....
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Transposed convolutional layer

Can someone define the weights in a transposed conv2D kernel used to perform interpolation (NN or bilinear or whatever)? The idea is to get "convinced" that one can perform upsampling (interpolation) ...

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