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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Graph of $[u(\tau)-u(\tau-4)]\cdot[u(t-\tau)-u(t-\tau-4)]$

I'm trying to visualize what would the following signal be like $$[u(\tau)-u(\tau-4)]\cdot[u(t-\tau)-u(t-\tau-4)]$$ Consider that $\tau$ is the independent variable here, $t$ is the shift variable. ...
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Implementing blind deconvolution in MATLAB

I want to implement blind deconvolution for the signal $ r(n) = h(n) \star s(n) + a(n)$ in MATLAB where $r(n)$ is the recorded speech $h(n)$ is impulse response of room acoustics $s(n)$ is desired ...
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How does MATLAB's $\tt upfirdn$ select extra points when downsampling?

I had a signal 512 samples long and I used upfirdn to filter and downsample it by a factor of 2. I thought this would result in a 256 sample long variable, but ...
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26 views

How many samples are identical in linear and circular convolution result?

Suppose we have two sequences $x[n]$ of length $L$ , and $y[n]$ of length $P$. If we are doing a $L$ length circular convolution between the two sequences ($L>P$), how many of the resultant samples ...
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37 views

How to overlap and add the frames after applying some modification in time domain

I am trying to apply Dynamic range compression (DRC) in time domain in MATLAB. But I am having problem in overlapping and adding the frames. Here is my work: ...
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59 views

When does the convolution of $2$ signals equals zero?

For example, how can I determine if the convolution of $x(t)$ with $y(t)$ is equal to $0$?
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29 views

How to calculate a Hann-LP kernel for image processing

I'm currently studying for an exam in image processing and stumbled upon a exercise which i could not answer and my professor will not be available before the exam anymore. The exercise goes as ...
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21 views

Feature maps for a Convolutional Neural Network

I hope this is the right place to ask this, so here goes: I am currently trying to implement a convolutional neural network in C++, but since I have no formal education in signal processing, image ...
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26 views

Calculate 2D Windowed Sinc Kernel

I am implementing a Windowed Sinc Filter for Scaling images by the factor of 2. Therefore I need to calculate a Filter Kernel. I already know how to calculate the kernel including a Blackman Window ...
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135 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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36 views

Convolution theorem for cross-correlation

Forgive me is this is an ill-posed question. Is there any such thing as a 'convolution theorem' for the cross-correlation. Namely, the convolution theorem states that: $$ x[n] * h[n] = ...
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40 views

How many non-zeros samples in convolution

If I have $b[n]$ of length 30 (30 non-zero samples) and $c[n]$ of length 40 (40 non-zero samples). How many non-zero samples will $a[n]=b[n] * c[n]$ have? (Note '$*$' is a convolution). I think ...
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28 views

Obtaining a frequency response from other frequency responses

I have loaded six impulses responses (1024 samples each in length) into Matlab, zero-padded the end of each with 1024 zeroes and taken 2048 point DFTs of each using Matlab’s built in ...
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3answers
89 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 ...
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2answers
50 views

What does convolution has the meaning? [duplicate]

As I know, if we want to know the LTI system output, then we do convolution between input x[n] and impulse response h[n]. but actually,in this question, I want to know what does convolution has the ...
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88 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 ...
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26 views

Concept check on doing multiply in time with circular convolution in frequency domain

So I think I have my thinking correct on what I'm trying to do, but I just want to make sure I'm not assuming something that isn't true. Below is what I'm currently doing in the time domain. $r(t)$ ...
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71 views

Do I have to flip my kernel when performing an FFT-based convolution?

I have a 2D image and I convolve it with a 2D kernel image using FFT. So far I was always using symmetric kernels (e.g., Gaussian with stddev_x = stddev_y). As a result, I never bothered thinking ...
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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 ...
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Convolution & FT properties

I have been trying hardly to check if these equalities are true or false. However, I have not been able to conclude anything. Could you help me, please? $$y[2n]=h[n]\star x[2n] $$ ...
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51 views

maching convolution filters to results

I am practicing for an exam and I need help in the following question (it is just for me- no grade...) we get an input image, 6 convolution filters and 6 results. we need to find the matches between ...
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57 views

What is the relationship between passivity of impulse response and passivity of the system?

What I mean by passivity of impulse response is that the energy of impulse response for this system is less than the input impulse signal energy. For example, in a discrete-time system, considering ...
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Does the output of this system have a closed form expression?

\begin{align} x(n)&=\left(-1\right)^n u(n)\\ h(n)&= u(n-1)+u(n-2)\\ y(n)&= x(n)*h(n)\\ y(n)&= \sum_{k=-\infty}^\infty \left(-1\right)^k u(k)\left[u(n-k-1)+u(n-k-2)\right] \end{align} ...
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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 ...
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Intuition behind impulse response terms in convolution

We're learning about convolution in my signals and systems class right now. I have been able to do all of the problems by simply working out the respective sum/integral, but I'm still having trouble ...
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63 views

2D Convolution Along Only One Axis and MATLAB Implementation

I'm trying to implement a Depth Map algorithm for Light Field images and I stumbled in a 2D convolution of an image and a kernel, but I think that the convolution is only preformed along the x axis. ...
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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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76 views

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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1answer
84 views

Question related to Discrete 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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1answer
100 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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74 views

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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446 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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70 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
48 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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26 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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2answers
103 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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37 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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1answer
54 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
407 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 half-band filters so each one has a cut-off at $\pi/2$. Then, I have to multiply the resulting signal ...
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1answer
50 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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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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1answer
64 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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1answer
34 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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117 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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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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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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28 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 ...