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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Unit step function present in convolution result

We are currently learning about convolution in my signals and systems class, and one of our textbook problems is to compute the convolution of $x(t) = e^{-\alpha t} u(t)$ and $y(t) = e^{-\beta t} ...
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Convolution by IIR filter, a case where circular convolution is allowed?

The question is, how to attain the frequency domain representation of any signal (which is finite, non-unit length) convolved with an IIR filter. The correct answer in my opinion is that there is in ...
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Question related to Disceret signal convolution

I have two finite signals $x[n]$ and $h[n]$, I want to convolve these signals using the method defined in Example 2.2 of Signals and Systems by Oppenheim. I am getting this answer $$ y[-3]=4, ...
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41 views

Find reappearing pattern in the signal

I am working with a signal that describes energy consumption in some house as a function of time and I am trying to find time intervals that correspond to some particular type of dish washer. What do ...
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FFT Convolution: missing sample somewhere

For a piece of software I've been working on lately I need to implement FFT convolution for performance reasons. Doing so has been mildly succesfull but there is still a error somewhere causing lots ...
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422 views

Why is convolution or FFT breaking in this case?

It is well-known that convolution in real space corresponds to multiplication in the reciprocal space. Yet, I obtain different results using both methods in the case that I'm going to present. I am ...
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60 views

Minimizing sinc spectral lobes

for some reasons I'd like to minimize the secondary lobes of the FFT transform of a rectangular signal (shwon in the upper-left side of picture below) so I've used window function to do that ...
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Is output of convolution of sinusoidal with itself, also sinusoidal? [duplicate]

Ladies, Gentlemen, In my last question I asked you present the convolution of sinusoidal with itself. I accept Mr Peter K.'s answer. Now my question is much more important. Is output of convolution ...
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Can you present the convolution of sinusoidal with itself?

Ladies, Gentlemen, Because I am homeless (in France), and get internet access only in public libraries with many restrictions in timing etc, I can not write down even a simple convolution. So I ask ...
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1answer
31 views

Overlap/Chunk processing possible with Zero-phase?

I'm relatively new to DSP and I'm currently investigating FIR filter and IIR filters. From what I've found FIR filters can be implemented efficiently using the overlap-save method, but I was wondering ...
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25 views

Magnitude of the circular convolution of a sequence with a shifted version of itself?

What is the magnitude $|y[n]|$ of the circular convolution of an 8 point sequence $x_1[n]$ and a one-shifted version of itself $x_2[n] = x_1[((n-1))_8]$ \begin{align*} y[n] &= ...
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93 views

Convolution in frequency domain

Simple math question. The convolution theorem states that multiplication in time domain is equal to convolution in frequency domain and vice versa. There is a condition that the signal has to be ...
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32 views

Approaching the response of an RC circuit via y=ifft(fft(x)fft(h)). Why is this valid?

Some textbooks like (Numerical recipes the art of scientific computing) derive the DFT as a Riemann sum of the CTFT. With this in mind it would be natural then to approximate the identity ...
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50 views

Creating a convolution kernel from filter description

I am not quite sure whether the question I am stating is right, or if I am trying to combine two not related topics but here it comes.. I am trying implement and apply a contra harmonic mean filter, ...
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1answer
131 views

How to cascade two filters?

I have to filter an audio signal through a cascade of two equal low pass FIR filters. They are halfband filters so each one has a cut-off at pi/2. Then, I have to multiply the resulting signal ...
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1answer
34 views

Concepts: Ideal and non-ideal channel resulting in intersymbol interference

I am following the book: Blind equalization and Identification by Zhi Ding and Ye Li. In Chapter 2, the concept of T spaced equalizers is presented. It is mentioned that the output of the channel is ...
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23 views

Enforcing size to match Convolution using 'same' property & Enforcing Circulant Matrix (Like DFT Based Convolution)

The original problem was from this link about coding de-noising an audio signal. Because my reputation points disabled me to comment, I have to ask a separate question here. I don't quite ...
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56 views

Using superposition and time invariance to find RL circuit response

I am confusing reading book by Chaparro (Signal System with Matlab) in example 2.7. He give a question, a RL circuit with unit-step source $ v(t) = u(t) $ will result response, $$ i(t) = (1- e^{-t}) ...
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33 views

How to solve a two variable equation of images?

I have two equations of images $$g_1=f_1+h_2*f_2$$ and $$g_2=f_2+h_1*f_1$$ where $*$ is convolution and $g_1,g_2,h_1,h_2$ are known. How do I find $f_1$ and $f_2$?
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Convolution Kernel Notation

I am applying convolution kernels to an m x n matrix as part of a fisheries survey data analysis (but this simply involves applying a convolution kernel to a matrix ...
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87 views

How to estimate filters using conjugate gradient?

An image $I$ is computed by performing convolution and summation: $$ \sum_{k=0}^{K-1} z_k * f_k = I $$ Given only the feature maps $z_k$ and the resulting image $I$, how do I compute the filters ...
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93 views

Limits of convolution

Say we have a function of time ($S(t)$) of the length $T$, and then a customized impulse response (say $I(t)$) of the length $T+N$. The question is, when $S(t)$ is convolved with $I(t$), what are the ...
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46 views

Convolution equivalent to matrix multiplication?

Is it possible to write the full convolution between the image and the filter as a matrix multiplication operation? If so, can someone give a simple example of how that works?
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22 views

Computing Convolution 2D

I am trying to compute convolution 2D I = [[2,0,1],[1,-1,2]], Filter = [[1,-1],[1,-1]] I tried to Pad zeros to the image to make it 3x3. It will be ...
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207 views

Auto Correlation vs Cross Correlation vs Convolution and their applications

I know from wikipedia that auto correlation in done on the same signal while cross correlation is done on different signals.But what does this actually imply in terms of application.I can always apply ...
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47 views

question regarding convolution theorem

As per the convolution theorem, a convolution in time domain is equivalent to a multiplication in the frequency domain. Then say (MATLAB code), ...
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98 views

Why does the amplitude of a discrete convolution depend on the time step?

I've just finished covering convolutions in my signals class, and I've been playing around with the conv function in MATLAB, but there's something I don't quite ...
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22 views

Is TOA is different for extended target?

The time of arrival (TOA) or time difference of arrival (TDOA) beteen two signals are seen extensively in literature. Are these algorithm applicable for point target as well as extended target? For ...
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4answers
128 views

Given a downscaled image, produce Gaussian blur of the original image

Let's say I a perform convolution of an image with a Gaussian kernel of some size. Is it possible to produce the exact same result from a downscaled version of the image? If so, what's its minimal ...
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144 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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113 views

gaussian filter close to image border

When applying gaussian filters close to the borders of an image, algorithms usually zero-pad or replicate/mirror/wrap the borders. This is not good enough for my case, so I wonder if there is ...
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50 views

Is there any library for convolution reverb software for Visual Studio besides Freeverb?

I am currently working on a simulation of a virtual scene. I calculate the IR of the direct path and the early reflections and want to convolute them with the input signal. My problem now is that ...
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62 views

Convolution reverb using a frequently updated frequency dependant impulse response

I am implementing a software to auralize a virtual scene but am kind of a newbie to DSP. The focus should be the calculation of the IR which is frequency dependant. But this means that the renderer of ...
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117 views

How to Actually Use FFT to implement Low Pass Filter

have searched high and low for a practical guide to implement a simple 50Hz low pass filter on a signal.I understand the theory but its the practical but that's missing. If I was using MATLAB it would ...
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26 views

Effects of simplifying normalized cross correlation equation

The normalized cross-correlation equation for images looks like this (from here): \begin{equation} \sigma(u, v)=\frac{\sum_{x,y}(f(x, y)-\bar{f}_{u,v})(t(x-u, y-v) - \bar{t})}{\sqrt{\sum_{x,y}(f(x, ...
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19 views

Detecting discontinuities in derivatives in images

Considering an grey-scale image as a function z=f(x,y). (Specifically, I'm interested in f=h∗h∗...∗h, where h is the indicator function of a regular hexagon.) I am interested in finding places where f ...
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Is the system $L\{f[m,n]\}= c[m,n] f[m,n]$ shift invariant?

$c[m,n]$ is the spatially varying gain. My prof says that its not shift invariant. However if we put $m=m-k$ and $n=n-l$ we get $c[m-k,n-l] f[m-k,n-l]$ which is how a shift invariant system should ...
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127 views

Circular Convolution of h(n)*x(n)

So I understand how Convolution works but Circular convolution seems a bit messy to me, all the examples seems to have even series of number like h(n)={1,2,3,4} & x(n)={1,2,3,4} and they are all ...
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59 views

Convolution theorem for “weighted” convolution?

Consider what I call a "weighted" convolution of a two-dimensional signal (image) with itself: $f({\bf r}) = \int d {\bf r}' \, g({\bf r}') s({\bf r},{\bf r}') g({\bf r}-{\bf r}')$ where $s$ is a ...
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1answer
50 views

How to simplify this sequence

So I had this question (f) at my last exam that I failed and I'm now studying for my re-exam, the problem is that I still don't know what the answer is supposed to be in this question (f): Do you ...
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43 views

Image processing using conv-neural net

Okay I am starting to understand the idea of neural networks but I still haven't been able to understand the use/benefits/implementation of convolutional neural networks especially for image ...
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12 views

What I am doing wrong when applying constrast sensivity function?

Physics explanation I am filtering an optotype image in order to simulate how a human eye would see it. I am not taking into account aberrations but only diffraction. The problem is that my ...
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35 views

Variation of Pulse width with center frequency in Pulse Compression technique

Assume a chirp with BW = 1 Hz (frequency range 0-1 Hz) for a period of 700 sec. The pulse compression technique (obtained through auto correlation function) applied on the chirp generates a pulse ...
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1answer
42 views

How to apply a 1D filter (CSF) to an image?

I am facing the following problem: I have an image and a contrast sentivity function (CSF). The CSF is a function defined in the frequency domain and it is just a band-pass filter. The problem is that ...
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31 views

Fourier domain division causing translation

I am trying to find the correct filter to convolve with an image so they have the same PSF. I have the final PSFs of both images: A: PSF of the image with the wider PSF. B: PSf of the image with ...
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Translation invariance in max-pooling and cascading with convolutional layer

I am reading through this page about convolutional neural networks and I am confused about the part about max-pooling (downsampling a signal/image with the maximum value in a block). Apparently, one ...
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45 views

Filtering with filters without even or odd symmetry in the fourier domain

I am doing a project where I have to use the fourier domain for convolution. I have been reading Digital Image processing by Rafael Gonzalez but I unsure about one thing, and I could not find anything ...
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What Is the Intuition of Convolution in The Signal Processing World [closed]

It is known that an LTI system is defined by its Impulse Response and the Convolution Operator. Could some put some intuition behind? Thank You.
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how to express a separable 2D convolution using properties like commutativity, associativity, etc?

I have two 2D sequence $x(n_1,n_2)=f(n_1)g(n_2)$ and $y(n_1,n_2)$. How can I express this convolution \begin{equation} x(n_1,n_2)*y(n_1,n_2)=(f(n_1)g(n_2))*y(n_1,n_2)=(f(n_1)*y(n_1,n_2))*(g(n_2)) ...
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1answer
141 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 ...