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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Convolution - Massive spike in noise section

I am computing the correlation with MATLAB using the convolution fonction with a signal flipped before feeded into the function. Here are the results. The first plot is the actual signal, the ...
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Confusion about adjoint of convolution

I have the following problem with convolution operators. I know that if I have a filter $g$, then the adjoint filter would be given by $h(x,y)=g(-x,-y)$, so that $\langle g * u,v \rangle = \langle u,...
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Why LTI system cannot generate any new frequencies?

Why $Y (\omega) = X(\omega)H(\omega)$ implies that an LTI system cannot generate any new frequencies? Why if a system generates new frequencies, then it is not LTI?
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How are convolution matrices designed? [closed]

I've been looking deeper into convolution filters for image processing, and I can't seem to find an intuition for how people come up with the matrices that people use. For example, edge detection. I ...
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2answers
35 views

The difference of downsampling an image and smoothing an image?

I am, at the moment, trying to read up on some simple computer vision elements, in which i have become a bit comfused on the terms downsampling and smoothing, and whether there is a difference between ...
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1answer
28 views

Smoothing complex data by convolution

I need to smooth noisy complex data with a Gaussian filter. Right now, I apply the filter to real and imaginary part of the data separately, which needs two convolutions. The intended results are the ...
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2answers
57 views

What is the difference between convolution filter, low-pass filter, and median filter?

Isn't blur filters, like median filter, a type of convolution filter? How does a low-pass filter relate to them? Why does this guy differentiate convolution filters here from blur filters here?
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How can I implement convolution in frequency domain?

Suppose, we have a bitmap image represented as a 2D integer array, int [,] image2D; whose FFT is Complex[,] fftImage2D; ...
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48 views

Upsampling with FIR filter causing discontinuity at start of new buffer [closed]

I have implemented an oversampling algorithm for an audio signal in C++ which is producing a distortion of the signal at the start of a buffer. The algorithm is wrapped in a class with methods for up ...
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25 views

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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42 views

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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25 views

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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27 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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1answer
46 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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1answer
69 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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1answer
45 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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0answers
23 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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34 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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149 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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41 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] = \sum_{k=0}^{...
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1answer
41 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
96 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
52 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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3answers
92 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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1answer
72 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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62 views

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? $$y[2n]=h[n]\star x[2n] $$ $$\mathfrak{F}(x[-...
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53 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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1answer
58 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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52 views

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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2answers
37 views

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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65 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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1answer
19 views

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 $y(t) = e^{-\beta t} u(t)$...
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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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1answer
100 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, y[-2]=...
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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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3answers
449 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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1answer
71 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 (bottom-...
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24 views

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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2answers
52 views

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
57 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] &= \sum\limits_{r=0}^...
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2answers
105 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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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 $$y(t)=x*h=\...
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58 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
497 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 (...