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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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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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31 views

duration for a signal

I am a beginner in the signal processing and I have questions for the duration of a signal. My system has a bandwidth $B$. I have a signal $s(t)$, the duration for this signal is $T$. The signal $s(t)...
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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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33 views

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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15 views

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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1answer
20 views

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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1answer
33 views

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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2answers
72 views

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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2answers
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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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62 views

Convolution of Two Impulse Signals

I have encountered convolution of two different impulse signals. ...
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3answers
128 views

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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1answer
43 views

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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2answers
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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
77 views

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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1answer
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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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1answer
52 views

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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1answer
49 views

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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2answers
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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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28 views

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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1answer
37 views

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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141 views

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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2answers
155 views

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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2answers
69 views

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 ...
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How to implement freq convolution layer?

I am referring the paper https://pdfs.semanticscholar.org/31c7/4962122ba5fe1c469101b5bc2ae6d88c9c18.pdf. In the paper, for CLDNN network first layer is freq convolution. How to implement the same for ...
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3answers
242 views

Deconvolution of Synthetic 1D Signals - How To?

I convolved a square wave with a Gaussian wave using linear convolution. Can I get the original square wave back by deconvolving my output with the Gaussian function? I took the FFT of both signals, ...
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35 views

Wide-Band Lorentzian FDTD Algorithm

I want to convert a simulated gain/absorption of a material, which can be understood as a discreet (dispersive?) function $g_i(f_i)$ ($f$ is for frequency) or $g_i(\lambda_i)$, into $\tilde g(t)$ for ...
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26 views

Convolution in the Hartley Domain

The convolution Theorem of the Hartley Transform is given by $$ Y_{Ha}(k) = X_{Ha}(k)H_{Ha}^{e}(k) + X_{Ha}(-k)H_{Ha}^{o}(k) $$ where, $$ H_{Ha}^{e}(k) = \frac{H_{Ha}(k) + H_{Ha}(-k)}{2} $$ $$ H_{...
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2answers
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Cannot figure out the convolution operation in this problem

A linear system S has the relationship $y[n]=\sum_k {x[k]*g[n-2k]}$, k ranging from $-\infty$ to $\infty$, between its input $x[n]$ and output $y[n]$, $g[n]=u[n]-u[n-4]$. Determine $y[n]$ when $x[n]=...
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24 views

Applying a filter on an input sequence in matlab

Given a input sequence $x = {x_1, ... x_n}$ and a filter with l elements $h = [h_1, ..., h_l]$ with l < n. We want to filter the input sequence with the specified filter. My first thought was to ...
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25 views

Resources for learning Sound Processing [closed]

Does anyone know of any resources that explain simply, these are the data objects and variable definitions involved when doing sound processing? I took a class on image processing where we learned ...
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63 views

Why convolution in time and frequency domain are not equal?

I was writing this Jupyter Notebook. Then, I unexpectedly faced two visually similar output, but their numerical results were very different. This is the code I used for convolution in the time ...
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2answers
70 views

Convolution of real with complex signal

Let $x[n]$ be real signal and $y[n]=\exp(j3\pi n)$ be a complex signal Would the convolution between those two signals be $$x[n] * \Re(y[n]) + jx[n]*\Im(y[n])$$?
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1answer
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How to find the impulse response of filter that outputs the autocorrelation of the input?

I am trying to solve question 9.61 in the attached image. I guess, by evaluating the autocorrelation for a specific instance, say $ t = 0 $ , that the impulse response, $h(t)$, should be : $$ h (t)...
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Convolution of signals sampled on a logarithmic grid

Is there a practical accelerated algorithm or a theoretical discrete (Fourier) transform based method to convolve discrete-time signals sampled on a logarithmic grid? What I mean is representing a ...
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1answer
67 views

How to increase the sharpness of the image using convolution matrix?

I am using 3 X 3 convolution matrix to obtain an sharpness image. But the output result obtain from the above matrix is not much sharpen image. How to increase the sharpness of the image ? Ya i am ...
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29 views

Convolution with rectangular function

I have a system $h(t)=4e^{-4(t-4)}u(t-4)$ and I want to response of the system to $x(t)=rect(2(t+4))$. I have followed those steps: $y(t)=x(t){*}h(t)$ $=rect(2(t+4)){*}4e^{-4(t-4)}u(t-4)$ $=4[u(t)-...