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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Convolution Theorem: Hamming Window on a Time Series and Fourier Domain

If we have a set of time series data, y, consisting of 100 data points. One can apply a N (odd) Hamming window as a weighted moving average to decrease the noise. Say, if we choose 7 point Hamming ...
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Does class imbalance affects for 1D CNNs?

I'm trying to develop a 1D CNN model for a high imbalance dataset. I tried giving sample_weights trying to compensate for the class imbalance. But it always classifies into one class.
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Making sense of indices in 2D convolution operations

Referring to the answer here: https://www.quora.com/Why-are-convolutional-nets-called-so-when-they-are-actually-doing-correlations, the equation for a discrete 2D convolution is specified as: $$C(x,y)...
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Is convolution distributive over multiplication?

Is there any formula or expansion for $$a(t)*[b(t) \cdot c(t)]$$ $$a(t) \cdot[b(t)*c(t)]$$ where $*$ denotes the convolution? By expansion I mean something like $a(t)\cdot[b(t)+c(t)]=a(t)b(t)+a(t)...
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Apodization in the Fourier (frequency) domain on discrete experimental data

Let us assume we had time domain signal as a raw data R (Window 1) and we wish to perform the deconvolution process on R using another set of raw data G (window 2). This is accomplished dividing FT of ...
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The Gradient of Least Squares of 2D Image Convolution

Given the objective function: $$ \frac{1}{2} {\left\| h \ast x - y \right\|}_{2}^{2} $$ Where $ h $ is the 2D convolution kernel and $ x $ is the 2D convolution image and $ y $ is a given 2D image. ...
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Find specific feature within an image / Neural Networks

i am working in the field of image processsing and we have a certain problem which is difficult to solve by rules-defined algorithms. Is it possible to teach a certain pattern into a neural network, ...
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Impulse response convolution and normalization2

when I take inverse Laplace transform of a system transfer function \ Lets say LPF whose TF is $H(s) = \frac{W}{s+W} $ the inverse Laplace/impulse response is $h(t) = We^{-Wt}.$ Now to see the ...
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Comparing arithmetic complexity of FFT radix-2 and convolution

Let's assume we have a discrete linear time invariant system and we have a real signal $x[n]$ with length N=50 as input for the system. The impulse response $h[n]$ of the system is considered to be ...
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Increasing error safety in the cross correlation of two binary signals in wireless communication

I want to cross correlate two binary signals, where one is corrupted by noise and shifted by a time constant $\tau$, but has the same bit pattern (so basically an auto correlation). Similar to case 2 ...
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Convolution property

Is the convolution of two equal signals the same signal? I have this system: and i have to find $h_1[n]$ (which i've been struggling for a while), given $$ h_2[n] = u[n] - u[n-2] $$ and $h[n] = ...
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What do the 1D filters represent when using imfilter?

I am reading the source code of an algorithm that is used to process an image. While reading this source code (and others), I've found lines of code of the form ...
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Bandwidth of a finite impulse response filter

In a machine learning application, a model learns to apply a filter h(n) via convolution to a 1-dimensional input signal s(n) (e....
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Is there a generalized method to get the input with the given output and the impulse response?

$y(t)=y(t+12), y(t) = x(t) \ast h(t)$ The continuous time signal output $y(t)$ is a periodic square wave, 50% duty cycle pulse. The impulse response is a box function.($A = 1, T = 2$) By using ...
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How to express STFT and ISTFT as a 1d convolution and 1d deconvolution in tensorflow/keras

I'm trying to implement this paper in tensorflow and keras. At the end of section 3 it says. ...
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DFT equivalent circular convolution weight matrix with a symmetric filter of length 2K+1

$\DeclareMathOperator{\diag}{diag}$In a research paper, I read that: For optimization, the $n\times n$ weight matrix of DFT can be equivalent to circular convolution with a symmetric filter of length ...
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After advice about detecting focus quality of objects in a photo detected using YoloV3

I've spent the last couple of days playing with YoloV3, and have had very good results. My use case is sports photography, and the object detection for people/bikes etc is very very good, I'm very ...
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Convolution library on Arduino

Does anyone know of a good convolution library in C++ that can be implemented on an Arduino. I'm using it to apply matched filters to a signal. Thanks, Luke
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Designing Matched Filters on Arduino

I'm trying to develop a prototype at the moment that includes a sensor to detect how fast someone is typing on a keyboard. Essentially this sensor is a microphone that will be able to detect keyboard ...
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How to Combine / Cascade two `3 x 3` Filters into One `5 x 5` Filter

If you have a uniform 3x3 box filter T which is: 1 1 1 1 1 1 1 1 1 And an 3x3 laplacian filter W which is: 1 -2 1 -2 4 -2 1 -2 1 Can these 2 filters be combined into one 5x5 filter, the ...
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why we use time step only in continuous convolution in MATLAB? But not in discrete convolution?

I am studying convolution from book of alex palamides but i am confused because he uses time step(in this case 0.01) in his code for continuous convolution as shown highlighted in attached photo but ...
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multiplication in frequency domain equals convolution in time domain mismatch

We know that a convolution in the time domain equals a multiplication in the frequency domain. As per the article below, https://www.dspguide.com/ch9/3.htm In order to multiply one frequency ...
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Is the convolution between a decomposition and reconstruction filter a scalar?

I'm very new in a research topic about wavelet filtering and I received an observation by a professor, but I actually cannot understand it, so I ask you to help me. Suppose to perform a stationary ...
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Requirement of time step in convolution output?

I am studying time domain analysis from book signals and systems labotary with matlab by alex palamides when i was studying convolution command topic on page 187, author discussed use of ...
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confused in difference between calculations of convolution and multiplication?

How are two signals multiplied? And how is it different from convolving two signals?? I have read the above question on dsp stack exchange and i also tried it in my matlab , code is as follow: ...
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Autoconvolution vs Autocorrelation

I have a serious doubt about Autocorrelation and AutoConvolution. My understanding is, Autocorrelation Autocorrelation is ...
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Circular Convolution Matrix of $ {H}^{H} {H} $

We all know that Discrete Fourier Transform (DFT) corresponds to circular (not linear) convolution. That is to say, if $x(n),h(n)$ and $y(n)$ is the original signal, the filter and output signal in ...
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Contradiction while using the convolution sum for a non-LTI system

In a recent quiz, we were given the following problem: The cascaded LTI systems $\mathcal{T}_1$ and $\mathcal{T}_2$ respectively have impulse responses $h_1[n]=\delta[n+3]$ and $h_2[n]=\delta[5−n]$....
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Reading a Wav File [closed]

I need to read two .wav files. One of them is a song, and the other one is impulse response. Then, I have to convolve them. In fact, I have read them by using ...
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Why can convolution only be applied to compute the output of a linear filter?

We apparently cannot compute the output of a bilateral filter (BF) using convolution (with the image) because the BF is a non-linear filter. In general, why can convolution only be applied to compute ...
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Interpreting results of multiplying signal and wavelets in the frequency domain

I have followed a lot of stuff on mike cohens website and have managed to make a filterbank of Morlet wavelets and convolve with an incoming block of samples. This of course is a computationally heave ...
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Why isn't bilateral filtering shift-invariant?

I have a source (that I can't share) that states that bilateral filtering isn't shift-invariant (that is, it depends on the input signal), hence we cannot use convolution and the Fourier convolution ...
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Convolution of Two Impulse Signals

I have encountered convolution of two different impulse signals. ...
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How Much Zero Padding Do We Need to Perform Filtering in the Fourier Domain?

Consider an $M\times N$ image $f$ and an $G \times K$ filter $h$. Given that convolution in the spatial domain corresponds to multiplication in the Fourier domain, then we can perform a convolution of ...
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Graphical DT Convolution

Attached is the question 1 part B, solution and my attempt. My attempt seems to be not correct. can someone comment?
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Can anyone please describe the relation between linear convolution and circular convolution? [duplicate]

It would be great if anyone could help. I am not able to find any relation amongst them, to me they are different things altogether.
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MATLAB - How do I get the Filter Function to get the output Energy Spectrum?

The image was from a question I posted on reddit, so ignore the title. I'm trying to write a program that plots these graphs I know that the first plot is just a plot of the source-signal so the "...
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1answer
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Why Does 2D FFT of Gaussian Looks More Sharper than Gaussian Itself?

I am trying to understand why 2D FFT is done on a Gaussian process in a particular code. From my understanding from these posts: https://www.researchgate.net/post/...
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What is the Fastest Way Ever to Do 2D Correlation?

Here is what i gathered so far: Any sliding window classification, image filtering or similar can be fastly done by a FFT (flip the signal and do convolution). Also, if the template/filter kernel is ...
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Wavelet Transform Implementation Method

I have been watching the wonderful youtube videos here: https://www.youtube.com/watch?v=4TTpwIZrUAo&list=PLn0OLiymPak2G__qvavn3T8k7R8ssKxVr&index=3 detailing morlet wavelets and fit ...
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Discrete Time Fourier Analysis

Suppose we're given the following: $ x[n] = 2 + (-1)^n $, and are given the impulse response $ h[n] = u[n] a^n $, of an LTI system where $ |a| < 1$. We're asked to find the output $y[n]$, if $x[n]$...
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Discrete Time Convolution Example

How did we get this final answer in example in fig attached. I understand that delta(n) is a DT unit impulse where it is 1 at n = 0 and zero elsewhere. I understand that u[n] is a unit-step where it ...
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HRIR and DT Convolution

You have an experimentally-measured HRIR and an audio signal. And you wish to implement filtering using scientific libraries in Python such as numpy, scipy and matplotlib(for plotting) Question A) ...
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What is the betwwen [i,j] and [u,v] in explinations of correlation and convolution (picture attached)?

I don't know how to write 'summation' symbol here hence posting the picture. Can someone explain to me the difference between i,j and u,v in this explanation of correlation and convolution? I know ...
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NLMS algorithm for a MISO structure

I am trying to implement an NLMS algorithm for a multi-input single-output(MISO) structure. We take a reference signal x, then we made a new set of P input signals from it as follows: x_op (k) = x(k)...
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How to find Fourier series coeffecients of convolution of two periodic continuous functions with different time periods?

Above given is my solution Plz check if it is correct and I got struck at last step .Plz help
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Confusion in the derivation of convolution formula [closed]

$$x(t)=\int_{-\infty}^{\infty}x(\tau)\delta(\tau-t)d\tau=\int_{-\infty}^{\infty}x(\tau)\delta(t-\tau)d\tau$$ Due to linearity, $$y(t)=T\{x(t)\}=\int_{-\infty}^{\infty}x(\tau)T\{\delta(\tau-t)\}d\tau=\...
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GCC-PHAT (Generalized cross correlation) always peak at delay=0 on real audio signal

I have studied the GCC-PHAT algorithm to estimate TDOA on audio signals at 2 mics. Here is my MATLAB implementation: ...
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For complex values, why use complex conjugate in convolution?

Taken from Adaptive Filter Theory (2014) written by Haykin page 110 : $$y(n) = \sum_{k=0}^{\infty} w_k^*u(n-k), \quad n=0,1,2,...$$ where $u$ and $w$ are complex values. My question is why use ...
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Support of the convolution of two rectangular signals

I'm trying to convolve two rectangular signals in the frequency domain $$H_1(\omega) = u[\omega +.2\pi] - u[\omega -.2\pi]$$ and $$H_2(\omega) = u[\omega +.1\pi] - u[\omega -.1\pi]$$ My result is a ...