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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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6answers
13k views

Flipping the impulse response in convolution

During convolution on a signal, why do we need to flip the impulse response during the process?
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10answers
29k views

Deconvolution of 1D Signals Blurred by 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 ...
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16answers
122k 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?
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4answers
41k views

What is the difference between convolution and cross-correlation?

I've found on multiple sites that convolution and cross-correlation are similar (including the tag wiki for convolution), but I didn't find anywhere how they differ. What is the difference between ...
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1answer
5k views

How to circularly shift a signal by a fraction of a sample?

The shift theorem says: Multiplying $x_n$ by a linear phase $e^{\frac{2\pi i}{N}n m}$ for some integer m corresponds to a circular shift of the output $X_k$: $X_k$ is replaced by $X_{k-m}$, where ...
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2answers
10k views

What is the difference between Difference of Gaussian, Laplace of Gaussian, and Mexican Hat wavelet?

There are three techniques used in CV that seem very similar to each other, but with subtle differences: Laplacian of Gaussian: $\nabla^2\left[g(x,y,t)\ast f(x,y)\right]$ Difference of Gaussians: $ \...
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1answer
3k views

1D Deconvolution with Gaussian Kernel (MATLAB)

Suppose that I know the output and the transfer functions of a system and I would like to calculate the input function using deconvolution. To get a grasp of the idea I have created a simple ...
5
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1answer
188 views

Difference between convolving before/after discretizing LTI systems

Suppose I have transfer functions for two continuous causal linear-time invariant (LTI) systems: $F_1(s)$ and $F_2(s)$. Let $D\left\{\cdot\right\}$ denote the function that maps a transfer function ...
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2answers
5k views

Sampling Theorem and Dirac Comb

I am reading "The Scientist and Engineer's Guide to Digital Signal Processing" and trying to understand Figure 3.5 below which is about the sampling theorem and aliasing. I do not understand the ...
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1answer
84 views

Applying Image Filtering (Circular Convolution) in Frequency Domain

To filter an image we can: Use a 3x3, 5x5, 7x7, etc. filter, that is convolve the image and the filter in the space domain. Use a FFT on both the image and the filter, multiply them together in the ...
0
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1answer
321 views

understanding discrete-time convolution in LTI systems

I'm trying to understand the discrete-time convolution for LTIs and its graphical representation. standard explanations (like: this one) start with the idea of decomposing an input signal $x[t]$ into ...
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1answer
36k views

Difference between correlation and convolution on an image?

Could you please clearly explain what is the difference between correlation and convolution that is done by a filter on an image? I mean in terms of signal processing definition I know that ...
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1answer
11k views

How are two signals multiplied? And how is it different from convolving two signals?

Suppose that I have two signals $x[n] = \left\{2,4,1\right\}$ and $p[n] = \left\{5,1,8\right\}$ and I want to multiply them. How do you do that? How different is it from convolving two signals? I ...
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1answer
1k views

How to find the convolution kernel in frequency domain?

I have a two vectors of spatial data (each about 2000 elements in length). One is a convolved version of the other. I am trying to determine the kernel that would produce such a convolution. I know ...
5
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2answers
3k views

Simulating analog filter using convolution or converting with fft

My task is simple; I want to simulate analog low-pass filtering of an input signal, using Python. Note that the input signal is an array of values, not an analytical function. My first question is if ...
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3answers
1k views

Sweep signal + microphone-recorded signal => Impulse response

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-...
2
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1answer
345 views

Convolution of $\sin(\omega t)$ and $\cos(\omega t)$?

If $x(t)=\sin(\frac{\pi t}{4})$ and $y(t)=\cos(\frac{\pi t}{4})$ then i need to find the Convolution $$z(t)=x(t) \circledast y(t)$$ So convolution will be $$\begin{align} z(t) &=\int_{-\infty}^{...
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1answer
323 views

Can two nonzero signals $x[n]$ and $y[n]$ give a zero convolution

Suppose $x[n]$ and $y[n]$ are two nonzero signals(i.e., $x[n] \neq 0$ for at least one value of n and similarly for $y[n]$).Can the convolution between $x[n]$ and $y[n]$ result in an identically zero ...
3
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1answer
1k views

Efficient FFT computation of a zero-padded vector

I don't think this question has a good answer but will ask nevertheless since it has been bothering me for a few days. I am interested in computing as efficiently as possible the N-point FFT of a N/2 ...
2
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3answers
2k views

Why unit impulse function is used to find impulse response of an LTI system?

Hello i am working in digital image restoration field, recently i have studied concept of convolution, i studied that to find the impulse response/point-spread function of an LTI system, an unit ...
2
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3answers
2k views

Get a N-FFT with two N/2-FFT already computed

After somme researchs on the web, I don't find the answer of my problem (or I don't understand it) and I hope this post will succeed. I'm working on a real-time FFT convolution algorithm (C++) which ...
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2answers
724 views

Fourier transform of a Fourier transform

I generate a Gaussian noise and then I filter it with a passband FIR Kaiser window filter. When I perform the Fourier transform of the output of the filter and plot its magnitude spectrum, it is ...
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1answer
3k views

When convolving two functions that are constants in a region and 0 everywhere else, where does the integration start?

Heads up, this is for homework. I never took a signals and systems course, so I'm behind on this stuff. I want to compute the convolution of two rectangular regions. I know the standard equation ...
3
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1answer
429 views

2D deconvolution of recorded electron beam data

I'm currently working on a project that involves using an electron gun and it would be really nice to know the spot shape of the electrons coming out of the gun (the frequency of electrons at some x,y ...
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2answers
3k views

When should the sum of all elements of a gaussian kernel be zero?

I found an approximation of a 5x5 2D convolution kernel like this : Here, the sum of the elements is zero and this one was used for Laplacian of Gaussian! Another one here : This one has all ...
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1answer
278 views

Filtering $ n \times n $ Images by Separable $ m \times m $ Filters. Computation Time for Filtering Using FFT, 2D Convolution and Two 1D Convolutions

Consider filtering square $n\times n$ images by square, separable $m\times m$ filters. Give general equations for the computation time for the following approaches to this: Filtering using FFT 2-D ...
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2answers
300 views

Need help understanding convolution indexing

Ok, this is leaving me increasingly frustrated. This builds on a previous question here but I am still not getting the indexing, although I learned from that question all the same. Case 1: First ...
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3answers
1k views

Convolution and windowing using a buffer - how do I do overlap add?

I'm reading chunks of audio signal (1024 samples) using a buffer, applying a Hanning window, doing an FFT on it, then reading an Impulse Response, doing its FFT and then multiplying the two (...
0
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1answer
167 views

Using the flip-and-drag method to draw a convolution

So, we are asked to graphically convolve (using the flip-and-drag method) the following pair of signals: $$x_1(t) = \delta(t+1)-2\delta(t-1) \ \ \ \ \ \ \ \ \ \ \ \ \ x_2(t) = \begin{cases} -1-2t, &...
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1answer
3k views

How do real-time convolution plugins process audio so quickly

Okay, so in Logic Pro I can load up a Space Designer plugin (convolution reverb) with an impulse that's 9.1 seconds long, turn my mic on, and get real-time convolution reverb as the mic records ...
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2answers
4k views

Standard Deviation in Gaussian Blur

I have a function that performs gaussian blur on image for some specific $\sigma$ (the standard deviation). It first computes kernel of size $\lceil 3\sigma \rceil$ and then performs convolution with ...
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1answer
305 views

Help Understanding Convolution Filter Formulation

I'm reading Computer Vision: Algorithms and Applications wich is available online as a PDF and on Chapter 3.2 page 111 it introduces convolution operators for images giving the formulation: $g(i, j) =...
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4answers
2k views

A better explaination for 'there's no flipping of the impulse response' [closed]

I showed the question about flipping the impulse response to some math teachers and electrical engineers at an university. They read Dilip's answer and thought that it was hard to understand what ...
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1answer
3k views

Exponential average with time constant of slow, fast and impulse

I have been studying about exponential average. There are enough explanations about this at Internet, but they do not explain about the time constant. I have one channel with a $T$ seconds time ...
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2answers
3k views

MOD-N Circular Convolution

How to find MOD-2 Circular convolution for the two sequences $h =[-1,3,-2,1]$ and $x = [1,-1,-2,1,3,2,1,2]$. I know the answer is $7$ $0$ from matlab but I don't know how to find it graphicly or ...
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4answers
2k views

Deconvolution by Convolution

This is now a second time I am attempting to ask this very important but simple question here. What I want to know is can you do deconvolution by convolving a signal. It is often stated that, for ...
4
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1answer
1k views

Common Use Cases for 2D Non Separable Convolution Filters

In the image processing world, I've noticed that a lot of the popular convolution filters are separable. Here's a quick list of common separable filters: Sobel Gaussian blur Box filter (all ones, for ...
4
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1answer
12k views

Get an input signal from LTI system output, find impulse response

I just study signal processing and I have some questions. How to find impulse response $h[n]$ sequence of the system if I have $x[n]$ and $y[n]$ (input and output) sequences? Hope there is a formula ...
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2answers
3k views

How to find the input if I have the impulse response and the output of a finite sequence?

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] = [...
2
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1answer
5k views

Deconvolution in Python

I'm trying to use and understand SciPy's deconvolve for a project I'm working on. I'm having some trouble understanding how to use it. What I would like to do is to take two PMFs from discrete ...
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2answers
4k 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}...
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1answer
1k 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
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1answer
259 views

Sharpen Defocused Image (Deconvolution / Image Restoration)

Using OCR, I want to extract text from product packages using Google Glass. However, because of the fixed focus of the camera the package pictures are blurred. Is there a way to sharpen the image? ...
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1answer
486 views

Ideal BandPass Filter

Let suppose x(t)=$\sum\limits_{k=-∞}^∞ R(t-kT)$ $R(t) = \begin{cases}1 &[0,2T] \\ 0 & \text{otherwise} \end{cases}$ x(t) is the input to an ideal bandpass filter with $\text{BandWidth} = \...
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2answers
912 views

Question about convolution in time and frequency domain

My question is about the number of data points when doing a convolution (or correlation) in the the time or frequency domain. let's say we have two signals, $a(t)$ and $b(t)$ each of length $16$. When ...
4
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1answer
6k views

Difference Between Linear Convolution and Circular Convolution

If I understood correctly (and this page should confirm: http://www.cs.ioc.ee/~khoros2/linear/convolution-teo/front-page.html) if I convolve linearly (the usual point-to-point multiplication and ...
3
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1answer
375 views

Fourier transform of Kernel Density estimate: convolution theorem?

I am reading this paper about density estimation (Appendix A), where the authors apply a Fourier transform to the estimated probability density (the $X_j$ are a sample of $N$ data points drawn ...
3
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2answers
107 views

What is the relation between kernel functions, kernels used in convolution and null spaces of a matrix?

I have recently started learning about machine learning and have come across kernels and null spaces. I understand that null space is the set of all vectors that satisfy the equation A.v = 0 (Where A ...
3
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1answer
212 views

Is it possible to simplify the convolution integral if the functions are non-zero in disjoint areas? [duplicate]

Possible Duplicate: When convolving two functions that are constants in a region and 0 everywhere else, where does the integration start? I have a function $f(x,y)$ and $h(x,y)$. $f(x,y)$ has a ...
2
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1answer
391 views

Exponential decaying step response in LTI System

I'm attempting to better understand the relationship between step responses, impulse responses, and convolutions. Say that I have a system where if I apply a constant input, my output decays from a ...