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.

Filter by
Sorted by
Tagged with
0
votes
1answer
232 views

Phantom harmonics when using cosine windows why do they appear and how to avoid them?

Given an L order cosine window, it is possible to show that the width of the main lobe is given by: $$\omega_w = \frac{2 \pi L}{(2N+1)}$$ Where $L$ is the order of the window, $N$ is the maximum ...
7
votes
2answers
106 views

Do $|s(t)|$ and $|S(f)|$ uniquely determine $s(t)$?

Consider a signal $s(t)$. My question is if you know $|s(t)|$ and $|\mathcal{FT}[s(t)](f)| = |S(f)|$ or equivalently $|s(t)|^2$ and $|S(f)|^2$ is it possible to determine $s(t)$? That is, is $s(t)$ ...
6
votes
1answer
376 views

Deconvolution Question on Article “Deriving Intrinsic Images from Image Sequences” by Yair Weiss

there are n derivative filters: $f_i$, and denote $f_i^r$ as $f_i$'s reverse filter such that $$f_i(x,y)=f_i^r(-x, -y)$$ $r_i, f_i$ given, to find $r$ from the equations: $$f_i * r = r_i, (1 \leq i \...
1
vote
1answer
225 views

Question About Linear and Circular Convolution - 1D and 2D

We know that applying a filter on an image is called correlation or convolution depending on the filter angle. In Gonzalez I have read that we can apply linear convolution on an image. Here I have a ...
0
votes
1answer
314 views

Filtering White Noise to Generate Harmonic Signal

I have studied convolutions and filters a long time ago. Today, I am trying to review the basics using some notes of mine, but I am finding difficult to solve easy problems. Since I don't have ...
0
votes
1answer
2k views

Recursive systematic convolutional code (RSC) realization in MATLAB

How can I implement $\rm RSC(2,1,2)$ in MATLAB? Can I use convenc function to build RSC? The convenc function has 2 arguments: ...
0
votes
1answer
143 views

convolve to differentiate black and white colors

a figure for instance of size 500*500 has half above part with black and below half white should result in a white line where the white meets the black (something like a single line at line 250 with ...
1
vote
2answers
62 views

How do I find the convolution of the following signals? [closed]

$h(t)$ is the inputted to convolve the $x(t)$ The signal written in unit step are: $x(t) = (5-t)u(t-3) - (5-t)u(t-5)$ $h(t) = 2u(t-1) - 2u(t-3)$ So to convolve I first change the function to: $h(...
1
vote
1answer
258 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)...
0
votes
0answers
13 views

Formula for PSD across an axis of a 2D output

Consider a 2D stationary input $e(x,y)$ and a 2D real convolution function $h(x,y)$. Let $S=h*e$ be the result of the convolution of $e$ by $h$. If needed, we may assume $e$ is isotropic (spectrum ...
0
votes
1answer
33 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 ...
0
votes
4answers
79 views

What does the convolution mean, what is the convolution philosophy [closed]

I would like to know why the convolution is necessary. that is, who said that multiplying numbers with others and then adding them would tell us something? If you could give me analogies without ...
4
votes
3answers
2k views

Estimating the Impulse Response of the Room Using Sweep Signal Microphone Recorded Signal (Input & Output of a Convolution)

I played this signal A (a 20Hz to 20000Hz sinusoidal sweep in 10 seconds) with a studio monitor speaker in a big church, and I recorded the result B with good microphones. The result is very reverb-...
0
votes
3answers
5k views

Deriving the Convolution Kernel of the Inverse of a Signal

Let $y$ be the inverse (in the sense of convolution) of $x$, i.e. $$x \star y = \delta$$ Context: $x[n]$ is a discrete signal defined for $n = 0,\ldots, N$. We can assume $x[n] = 0$ if $n \not\in [...
4
votes
1answer
2k views

How Can Convolution and Deconvolution be Defined for 3D Images?

I am trying to understand how convolution and deconvolution can be represented for 3D images/ stacks of data. I would prefer it, if you built the these concepts from 1D vectors to 3D matrices in terms ...
3
votes
2answers
4k views

How to Estimate the Input for a Convolution Given the Filter (Impulse Response) and the Output of the Convolution

I understand how to find the output from the input with an impulse response, but how can I go about finding the input if given the other two? I have $y[n] = [-1, -1, 11, -3, 30, 28, 48]$ and $h[n] = [...
5
votes
3answers
5k views

An Intuitive Way to Understand the Sharpen Convolution Filter in Image Processing

Can someone explain sharpen in a non-technical way. So, I don't mean that you need to multiply every pixel with 5 and subtract it with the pixel left, under, above and right.
11
votes
4answers
16k views

How Does a Convolution Can Be Expressed as a Matrix Multiplication (Matrix Form)?

I know this question may not be very relevant to programming, but if I don't understand the theory behind image processing I'll never be able to implement something in practice. If I got it right ...
-1
votes
4answers
331 views

A Music Recommender System by Using Basis Functions and Inter Correlations

So my university project is about music recommender system. My teacher not saying too much. But he only said it will use basis functions and convolution technique. I want some ideas about this ...
11
votes
12answers
31k views

Deconvolution of 1D Signals Blurred by a Gaussian Kernel

I have convolved a random signal with a a Gaussian and added noise (Poisson noise in this case) to generate a noisy signal. Now I would like to deconvolve this noisy signal to extract the original ...
5
votes
2answers
107 views

2D convolution of image with filter as successive 1D convolutions

I want to prove (or more precisely experiment with) the idea that a 2D convoltion as produced by the Matlab conv2() function between an image I (2D matrix) and a kernel (smaller 2D matrix) can be ...
0
votes
0answers
15 views

DFT of a function and array convolution

I saw some questions (and answers) on this subject, but they were all about a specific example and I'm not sure I understood. I'm trying to understand the meaning of computing the DFT of an array ...
51
votes
17answers
138k views

What is the physical meaning of the convolution of two signals?

If we convolve 2 signals we get a third signal. What does this third signal represent in relation to the input signals?
6
votes
1answer
258 views

Analytical Expression for Convolution of Two 2D DFTs

I am trying to do an image analysis problem on some images, and I want to calculate some things in the frequency domain which are giving me problems. Say I have an (discrete) image $I(x,y)$ of size $...
5
votes
3answers
1k views

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 ...
0
votes
0answers
40 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 ...
2
votes
3answers
376 views

Band-pass filter doubles the frequency

I ran into a strange bug while implementing a complex band-pass filter. The filter design process is based on the windowing method and seems to be working well, but when i apply the coefs of the ...
2
votes
1answer
57 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 ...
0
votes
3answers
2k views

Principal Component Analysis (PCA) on Convolutional Neural Network (CNN) Features

Please, I have a question regarding PCA and features which are extracted from a convolutional layer. link if we have a test dataset , and we extract all conv features of all images at test dataset ...
0
votes
2answers
50 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 ...
1
vote
2answers
5k views

How to Prove a 2D Filter Is Separable?

I want to prove that 2D Gaussian filter is separable and we can separate it into two dimensions, my problem is about the size of filters. we should prove that $G(x,y)*I$(where $G(x,y)=$$\begin{bmatrix}...
1
vote
1answer
40 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 ...
1
vote
1answer
357 views

Use Scale Space Representation to Filter Single Image

Currently I hope to use scale space representation to filter one image. Features in one image can be filtered using an Gaussian smooth filter with one optimal sigma. It means different features in one ...
2
votes
2answers
102 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 ...
1
vote
2answers
6k views

Applying Lowpass (LPF) and Highpass (HPF) Filters to an Image in Frequency Domain in MATLAB

What I want is simply to apply low pass and highpass filters to an image in the frequency domain. Does MATLAB image processing toolbox have any commands for this?
1
vote
1answer
46 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 ...
1
vote
2answers
80 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 ...
5
votes
4answers
745 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 ...
0
votes
1answer
75 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 $...
0
votes
1answer
2k views

Generate the Matrix Form of 2D Convolution Kernel

We know that a convolution can be replaced by a multiplication with a toeplitz circulant matrix. Meaning, assume I have convolution kernel $h$ and matrix $I$ (of size $m \times m$ for example), then ...
0
votes
0answers
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 $A(f)$, $B(f)$,...
1
vote
1answer
73 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 ...
0
votes
1answer
18 views

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 ...
0
votes
2answers
49 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 ...
1
vote
1answer
42 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. ...
4
votes
2answers
169 views

Filter design to realize Cauchy product

I come from Computer Science so please pardon for my possibly wrong terminology. I need to design a filter which has coefficients $$h_0, h_1, \ldots, h_n, \ldots \quad\text{such that}\quad h_0 > ...
2
votes
0answers
41 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: \...
0
votes
1answer
57 views

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 ...
0
votes
3answers
69 views

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 ...
3
votes
1answer
46 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 ...