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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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33 views

turn circular convolution into linear convolution by zero padding: A special case

We know that, multiplying a kernel and signal spectrum in Fourier domain will lead to a circular convolution and not a linear convolution, so in order to it become linear convolution we must zero pad ...
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3answers
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How do impulse response guitar amp simulators work?

I am wondering how impulse response guitar amp simulators/modelers work. I thought it was a matter of convolving a signal of recorded impulse response in time-space with a guitar sample. I tried to ...
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1answer
54 views

Deriving the Langrangian interpolation polynomials in Cook-Toom convolutions

I'm working through Blahut's 'Fast Algorithms for Signal Processing'. Trying to develop an intuition for the Cook-Toom algorithm for convolutions as used by Lavin and Gray in their Winograd paper for ...
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1answer
25 views

DTFT of window function applied to input signal

$$x[n] = cos(\omega_1n) + cos(\omega_2n)$$ $w[n] = 1/N$ for $0 \leq n < N, 0$ for everything else Find the DTFT of $y[n]=x[n]w[n]$ expressed by the DTFT of $w[n]$, $W(\omega)$ I was thinking ...
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Proof of derivative of convolution $(h * f)' = h' * f$ [duplicate]

I have a convolution $h * f$ and I should proof $$\frac{\partial}{\partial x}(h * f) = (\frac{\partial}{\partial x}h) * f$$ but I can't know how to proof it.
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2answers
49 views

When to apply circular convolution formulas?

Context I am studying the family of Discrete Trignometric Transforms (DTT): Discrete Cosine Transforms (DCT) and Discrete Sine Transforms (DST). And trying to understanding more their properties, I ...
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1answer
35 views

How is 2D convolution calculated?

I wish to implement the 2D convolution on an FPGA, so Ineed to understand how it is calculated in practice. The main difficulty that I found apparently 2 different ways showcases how to do it. The ...
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1answer
43 views

Convolution Integral of Harmonic Signal (Cosine) with the Sinc Function

I was asked to show that this convolution integral results in the answers also given in the image. Not quite sure how to approach this integral, everything seems to be coupled together. Does anyone ...
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2answers
60 views

Shift vector function in MATLAB

I am working on my own shift vector function that will be used later to compute the convolution of two signals. The function has to shift the vectors either left or right depending on the magnitude ...
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4answers
742 views

Can every type of linear filter be modelled by a convolution?

I have an input time series going through a filter that creates another time series as output. If I assume in first approximation that my filter is linear, does it necessarily mean that I can model ...
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2answers
92 views

Convolution of Signal with a Gaussian Filter / Kernel

Following up on Analytical Solution for the Convolution of Signal with a Box Filter, I am now trying to convolve a Gaussian filter with the sine signal by hand. My method is to use the definition of ...
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41 views

Solving equation with convolution

I have the measured signal $y(t)$ that can be modeled in the frequency domain as $Y(f)$: $$Y(f) = X(f)\cdot A(f) - [X(f)\cdot B(f)] \ast C(f)$$ where $\ast$ is the convolution. I know $A(f)$, $B(f)$,...
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1answer
69 views

What is the peak resonance of convolving with a sine FIR filter?

I'm trying to improve my understanding of FIR filters. As an experiment, I've manually created an FIR filter, whose coefficients follow exactly one period of a sine wave. I'm wondering what is the ...
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1answer
73 views

Analytical Solution for the Convolution of Signal with a Box Filter

I have an exercise in which I am trying to filter an input signal $y(x) = \sin(x)$. Ideally, I would like to apply a box filter to this signal. Previously, I successfully convolved the input signal $...
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1answer
40 views

Partitioned overlap-add convolution - strange behavior at buffer boundaries

I've implemented a convolution reverb that operates in real-time, one audio buffer at a time (using FFTS for the fft bits). However, there's some strange behavior at the start of every buffer. ...
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37 views

Understanding convolution of Chirp z algorithm

I dont´t understand how works the convolution part of the Chirp z. I understand how the DFT is transformed \begin{align*} x(k) = \sum_{n=0}^{N-1} x(n) W_N^{kn} \end{align*} to this expresion: \...
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1answer
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How does minimum-latency partitioned convolution reverb work when you receive input samples in chunks, rather than one at a time?

I'm writing a reverb system where I receive an input block of samples 480 elements long, do some operation on them, and pass the block on to the next effect. I've been reading up on partitioned ...
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1answer
43 views

Representing a continuous LTI system as a discrete one

I am aware that there are different ways to represent a continuous time system in discrete domain (e.g. bilinear transform, impulse invariance transform). But my problem is as follows: Given an ...
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2answers
46 views

Why Are There Two Different Common $ 3 \times 3 $ Kernels for the Laplacian?

I find both of these 3x3 Laplacian kernels to be commonly used: 0 -1 0 -1 4 -1 0 -1 0 and: -1 -1 -1 -1 8 -1 -1 -1 -1 ...
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3answers
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Why do convolution kernels such as Gaussian, Laplacian, LoG almost always seem to be expressed in integers?

I'm a total newb in search of some deeper understanding, but I'm not able to read the maths behind these on Wikipedia. If I understand correctly, you get the new value for each pixel by multiplying ...
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1answer
39 views

Convolution between two vectors. Length and normalization

I have an RIR vector $h[n]$ with $N$ samples and an audio source $x[n]$ with $M$ samples. I wish to simulate a 5 seconds audio segment with $x[n]$ randomly located within (timewise). Using MATLABs <...
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1answer
28 views

Difference between the two forms of input-output relationships of an LTI system

$$y(t)=f(t)*h(t)\tag{1}$$ $$y(t)=H(s)e^{st}\tag{2}$$ $$H(s)=\int_{-\infty}^{\infty}h(t)e^{-st}dt\tag{3}$$ Let $f(t)$ in Eqn $(1)$ be $e^{st}$. In many worked out examples, I have found that the two ...
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1answer
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Faster Algorithm to convolve/correlate two sparse 1-D signals in python (or any language)

I have two signals which I need to correlate or convolve. Each signal is sampled non-uniformly and the values of the signal I have with me are the timestamp and the magnitude of the signal at that ...
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4answers
71 views

Determining LTI system response to a scale change

We know that for an LTI system, if $y(t)$ is the output for $x(t)$ then the response for $x(t-2)$ will be $y(t-2)$ and so on. But my question is what will be the system response for the input $x(-2t)$...
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1answer
36 views

MATLAB Convolution

I am designing an IIR notch filter using pole-zero placement method. I am trying to convolve the two zero locations using ...
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1answer
29 views

Conflict with the properties of convolution

excuse me in advance for the lenghty question, consider the following signals: $x_1[n]$, $x_2[n]$, $y[n]$ and $z_1[n] = x_1[n] * y[n]$ $z_2[n] = x_2[n] * y[n]$ In addition, we know that: $x_2[n] =...
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1answer
37 views

How to convolve $u(-t)$ with other signals?

How can I convolve the following $u(t+1)*u(-t)$ I know that convolution with $u(t)$ gives the integral of a function but what change occurs due to $u(-t)$?
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1answer
60 views

Serial filtering using FFT

lets say I have 3 audio filters for a realtime DSP application. For simplictity each has length 256 (as well as the input signal). The filters should work in series. Starting with filter IR h1(n) and ...
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1answer
56 views

What is the point spread function and optical transfer function and what uses are they in image processing

So I seem to really be struggling with the concepts of the point spread function (PSF) and optical transfer function (OTF) and what they are used for in image processing. Everything I seem to google ...
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1answer
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Given local responses by a bank of equally spaced (log-)Gabor filters, how can we estimate the response of an intermediate-scale filter?

Consider a grayscale image convolved with a bank of 2D wavelet quadrature pairs – in my case, log-Gabor filters. I have eight filters. For simplicity, let's say they are all vertically oriented, and ...
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61 views

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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2answers
64 views

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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1answer
202 views

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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2answers
45 views

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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1answer
73 views

Impulse response convolution and normalization2

when I take inverse Laplace transform of a system transfer function \ Lets say LPF whose TF is $$\frac{Y(s)}{X(s)} \triangleq H(s) = \frac{W}{s+W} $$ the inverse Laplace/impulse response is $$h(...
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1answer
165 views

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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19 views

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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2answers
66 views

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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2answers
77 views

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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1answer
68 views

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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1answer
43 views

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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0answers
35 views

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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4answers
143 views

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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113 views

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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1answer
111 views

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 ...