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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Approximating inverse of unstable difference of Gaussians filter

I am trying to invert a difference of Gaussians (DoG) filter. The inverse is not stable and so I am trying to find an approximation applied to a specific input. The DoG filter increases contrast at ...
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1answer
39 views

Is it possible to tune parameters/coefficients in convolutions similarly to linear models?

Is it possible to tune parameters/coefficients in convolutions similarly to linear models? I.e. to tune it to desired responses on the go. What confuses me: convolution is a complex "learning&...
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62 views

Impacted of a conjugated filter

What is the effect of using a conjugated FIR filter? I have a use case where a weight vector, x, can be estimated using the least squares approximation: $$Ax=b$$ $$ A^HAx = A^Hb$$ $$ x = (A^HA)^{-1} ...
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1answer
43 views

How to Use Convolution Theorem to Apply a 2D Convolution on an Image

How do I actually apply the convolution theorem? I have my fourier transformed image matrix, and a Fourier transformed kernel, but how do I actually multiply these together to achieve the intended ...
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1answer
58 views

Prove Convolution Property for DFT using duality

If $x_1[n]$ and $x_2[n]$ are finite length sequences of length $N$ $$\mathcal{DFT}(x_1[n] \circledast x_2[n]) = X_1[k]X_2[k]$$ where $X_1[k]$ and $X_2[k]$ are the DFTs of$x_1[n]$ and $x_2[n]$, ...
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44 views

Prove Discrete Time Fourier Series Multiplication property

Note: This is not a homework problem. I'm just stalled at a point because I think I might be interpreting the duality property incorrectly. If $x_1[n]$ and $x_2[n]$ are periodic with period N, then if ...
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27 views

What does shift and multiply-accumulate mean in terms of Convolutional Neural Networks?

While reading this paper, I came across the following paragraph - "Our intuition is: the convolution operation consists of shift and multiply-accumulate. We shift in the time dimension by ±1 and ...
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2answers
25 views

Real time estimation of room impulse response using the sine sweep method

I am working on real time Room Impulse Response estimation using sine sweep. $x(n)$ is my sine sweep signal. $f(n)$ is its amplitude modulated inverse. $beep$ consists of 3 sine sweeps with a delay ...
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26 views

How can we find Room Impulse Response in real-time using Sine Sweep Method?

I want to calculate the room impulse response in real-time using sine sweep method. For that, I generated a sine sweep $x$ & its amplitude modulated inverse signal $f$. Then I played that $x$ ...
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1answer
36 views

On discrete fourier coefficient convolution of indivdual periodic signals with different frequencies

It is a well-known result that when two signals with the same period $T$ get multiplied in the time domain, the resulting signal's Fourier coefficients are given by the discrete convolution of ...
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1answer
52 views

log(conv) vs conv(log)

Suppose an arbitrary, strictly positive $x[n]$, transformed as $$ x_l[n] = \log(1 + C x[n]) \tag{0} $$ where $C$ is freely chosen. Given the following, where $h[n]$ is a Gaussian lowpass filter (or ...
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Prove that the twisted Convolution of $f$ and $g$ lies in $L^2(C^n)$?

Edit,this is the exact phrasing of my question Let $\lambda\in\mathbb{R^n}$.Prove that $f\star_{\lambda}g\in L^2(\mathbb{C^n})$ for all functions $f$ and $g$ in $L^2(\mathbb{C^n})$.What Happens when $...
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Convolve with a box filter in time domain

To low pass filter a signal, we have to convolve it with a sinc function because it's the same as multiplying the Fourier transform of the signal with a rect function, resulting in the high frequency ...
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1answer
49 views

How this convolution integral is solved to obtain autocorrelation function of current for shot noise?

I am studying shot noise characteristics from this source: Here the author writes that autocorrelation function is given by: $$R_I(\tau)=\bar{h}*h*R_Z(\tau)$$ where $R_Z(\tau)=q^2(\lambda^2+\lambda \...
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Multiple 1D gaussian filter

Given $$ \begin{cases} &f_0(x)=1 \\ &f_{n+1}(x)= (\varphi*(f\mathbb{I}_{[a_n,b_n]}))(x)=\int_{-\infty}^{+\infty}\varphi(x-t)f_n(t)\mathbb{I}_{[a_n,b_n]}(t)dt = \int_{a_n}^{b_n}\varphi(x-t)f_n(...
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2answers
372 views

Generate the Matrix Form of 1D Convolution Kernel

As a follow up to Generate the Matrix Form of 2D Convolution Kernel, could someone explain how to generate the matrix form of a 1D convolution kernel? How different convolutions shapes are handled? ...
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1answer
61 views

Fast computation of a convolution integral with Gaussian kernel

Given a convolution integral with gaussian kernel $$ g(y) =\int_a^b\varphi(y-x)f(x)dx=\int_{-\infty}^{+\infty}\varphi(y-x)f(x)\mathbb{I}_{[a,b]}(x)dx $$ where $\varphi(x)= \frac{1}{\sqrt{2\pi}}\exp{\...
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1answer
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Perform Transposed Convolution in Spectral / Frequency Domain?

I'm doing some experimentation on performing end to end generative modeling in the frequency domain. I've got a working convolutional layer, but do not yet have a Conv2DTranspose equivalent. Please ...
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44 views

convolving an LTI with filters

I just started learning signal processing and one of the very first topics I begun with is convolution. I want to learn signal processing practically, therefore I opted to work with circuits(also a ...
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2answers
76 views

Convolution between a channel with real signal vs. channel with complex signal

The real transmitted signal $x(t)$ is convolved with channel $h$ in passband as : $y(t) = x(t)cos(j2πf_c t) * h(t)$ = $Re(x(t)e^{j2πf_c t})*h(t)$ where $f_c$ is the carrier frequency and $t$ is the ...
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1answer
64 views

Why aren't the integrator and the differentiator inverse systems?

I have a statement that leads to a paradox, but I'm incapable of finding the part where I'm wrong. The integrator system $$x(t) \mapsto y(t)=\int_{-\infty}^{t}{x(\tau) \, {\rm d} \tau}$$ is a linear ...
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How to update point spread function of blind deconbolution by conjugate gradient?

There is an unblurred image $g$ and a blurred image $x$. Their relationship is expressed by the following formula using $psf$(point spread fucntion, size is $5×5$ kernel). $g = x \otimes psf\tag 1$ ...
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Is there any complex-valued function used to smooth signals?

To obtain a smoother signal, we usually convolve the original signal with a real-valued kernel function, such as Gaussian and Top-hat. Is there any complex-valued kernel function to smooth signals?
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Linear Phase Filters and FFT

The FFT decomposes a signal into cosine and sine functions, respectively, even and odd components of the signal. Hence, I would expect even symmetric filters to have zero imaginary parts. Suppose a ...
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1answer
39 views

Identify out signal from in signal and impulse response

Hi there I am studying a course in signal processing and systems. I was given an excecise which I am having a great deal of trouble solving. I am allowed to solved using matlab, but for top marks I ...
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real time - active noise control

I am trying to implement an adaptive filter for system identification and active noise control for realtime signal processing on an FPGA using Labview. For system identification, I implemented the ...
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1answer
58 views

How to compute convolution using the Discrete Hartley Transform

It's easy to compute the Discrete Hartley Transform of a 1D signal: ...
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1answer
51 views

signals and systems,matched filter concept

The system with impulse response hi(t) is known as the matched filter for the signal Xi(t) because the impulse response is tuned to xi(t) in order to produce the maximum output signal. My intuition ...
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2answers
150 views

Deconvolution of system response in Python/Matlab

I had two sets of data, the output function of the system (time series with a length of 1292 entries) and the transfer function (similar to a gaussian with a length of 681 entries). I would like to ...
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how to get N point FIR filter( convolution) output when input and impulse response are both N points ? ideally convolution results in length N+N-1

x[n] -> Input Signal of length N h[n] -> Impulse response of length N y[n] = x[n]*h[n] (convolution to get the output of this FIR filter) Ideally length of y[n] should be N+N-1 but is it ...
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65 views

Convolving a LP FIR filter with a HP FIR filter

I currently feed a sampled audio input signal into a 511 tap highpass FIR filter, the output of which is then fed to another 511 tap lowpass FIR filter, resulting in a very narrow bandpass filter ...
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2answers
70 views

Energy-preserving convolution kernel?

Is there a function, in continuous or (primarily) discrete time, such that convolving with it preserves the input's energy? For $x$ that is finite-valued, finitely supported in time, and: Real or ...
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2answers
41 views

Moving average filter using DF-I and DF-II

I understand that the moving average filter is simply the average of a number of points from the input signal to produce the output signal. If x[] is the input and y[] is the output and M is the ...
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2answers
34 views

Deconvolution of shifted gaussian function in the frequency range

I have a signal defined as $$A(t)\cdot\exp\left(-i\omega_0t\right)$$ with $A$ the envelope function and $\omega_0$ the carrier frequency. I would like to transfer this signal into the fourier space ...
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1answer
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Replicate MATLAB's `conv2()` in Frequency Domain

When conv2d is on same mode, the image needs no padding, because the result is the same size as the image. When ...
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2answers
91 views

FIR Filter design, using different filter length than signal length

Given some neurophysiological application I am filtering in real time data of limited length (e.g. in epochs of 100 ms) using a sampling rate of e.g. 100 Hz. Due to this short time segment I am trying ...
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67 views

Convolution Reverb Calculation

Here's my basic understanding of how to implement a convolution reverb: I measure the IR of a space using a sine sweep. The raw mic output is stored as a Voltage-Time data set. Let's assume that this ...
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115 views

Boundary effects with scipy.fftconvolve after convolution

I am having some numerical error in my code that propagates continuously, and has to do with the implementation of convolutions in Python; this is kind of struggling my progress and I would really ...
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2answers
125 views

Equalizing audio under linux / Raspberry Pi

I have an audio streaming receiver written in Python running on a raspberry pi. This receiver writes the streamed audio out to an alsa device, which in turn passes it to an amplifier which is driving ...
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2answers
87 views

Under what conditions is the convolution of an input signal with the system's impulse response periodic?

I'm currently solving the following convolution problem from Oppenheimer's book: In the solution, it was stated that "$x(t)$ periodic implies $y(t)$ is periodic" So I wondered if it's ...
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21 views

Filtering relationship for sources propagating over a sensor array

A sensor array $y$ measures the superposition of $N$ sources $s$, at time $t$ and position $x$ we have : $$y(t,x)=\sum_{i=1}^{N} s_i(t,x)$$ The sources $s$ travel at constant speed over the array of $...
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2answers
74 views

Calculating cross-correlation using Walsh-Hadamard transform

I am trying to implement MLS method of measuring impulse responses. There is an article describing the method: http://www.commsp.ee.ic.ac.uk/~mrt102/projects/mls.... As I understand, to get an impulse ...
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2answers
44 views

Physically, what does the usage of two variables mean for convolution

My intuition of convolution is that it is just a way to depict multiplication of two signals where each signal is made up of various frequencies and phases. Since it isn't easy to find the value of $\...
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56 views

Image convolution using FFT

I just can't get my head around Fourier transform and convolution in 2D. I am trying to implement image convolution using fast Fourier transform (in julia). So the first thing I need to do is to pad ...
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0answers
55 views

Combining signals in MFCC space

I'm looking at a data augmentation method for training up a neural network of speech data. Currently I have two version of augmentation. The first method works by taking an audio file and mixing in a ...
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1answer
67 views

bit reversed order of FFT matrix for channel estimation

Although the question seems similar to this one HERE, but what I want to ask about is little bit different. Assume we have a signal $X$ whose length is $N$x$1$, we convert that signal into time ...
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1answer
45 views

Channel estimation using bit reversed order of FFT matrix

Is it possible to use the bit-reverse order of FFT instead of FFT to estimate the channel? Based on my reading, I found that bit reversed order of FFT matrix can diagonalize the channel, but ...
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1answer
92 views

Scaling the input vs scaling the impulse response for an LTI system

Two different cases: We pass $x(t)$ to an LTI system with impulse response $h(2t)$ and get the output $y(t)$. We pass $x(2t)$ to an LTI system with impulse response $h(t)$ and get the output $z(t)$. ...
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Upsampling class activation maps for discriminative feature localisation

I am currently reading a paper by on learning deep features for discriminative localization where the authors propose to use class activation maps to learn discriminative localised features. The ...
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39 views

convolution of two exponential signals with imaginary numbers

I can solve problems without imaginary numbers, but when exponential contain imaginary numbers, I can't solve the problem. For example, $x(t)=e^{3jt}+e^{4jt}$, $y(t)=(e^{-3t}-e^{-4t})u(t)$ (where $j$ ...

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