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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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1 answer
61 views

Signal Processing of Long Term Behavior in Stochastic Systems

I am quite new to techniques of signal processing. I have a fairly generic problem and wish to find information about topics and/or techniques that may help me address this problem. Let $x(t)$ and $y(...
0 votes
0 answers
49 views

Is it some kind of numerical instability for this convolution product (C language)? [migrated]

I am trying to program a convolution product function in C language. I am generating sine waves with the following function: ...
3 votes
1 answer
53 views

Is there any meaning to the extra-points introduced by a convolution product?

Mathematically speaking, when convolving a $N$-points signal with a $M$-points signal, the resulting signal contains $N+M-1$ points. In practice, the $N$-points signal may be an audio signal to which ...
1 vote
1 answer
257 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 ...
0 votes
1 answer
100 views

Is it possible to transform a pointwise product into a convolution?

Let $A(k)$ and $B(k)$ be signals in the wavenumber domain. Is it possible to find a function $G(k)$ such that $G(k) \ast B(k) = A(k)B(k)$? Preferably a closed form solution. I tried the following ...
1 vote
1 answer
325 views

How to perform an analytical computation of the convolution sum for a discrete-time system?

I am trying to follow some notes on "Analytical Computation of the Convolution Sum (Graphical Method)" but am getting stuck on what I am doing, or if what I am doing is correct. There are 5 ...
2 votes
4 answers
415 views

Convolution of sinusoid and running sum filter of order 5

Problem Compute analytically the convolution between the impulse response of a running sum filter of order 5 and a sinusoid $\sin(20\pi t)$ sampled with $f_s = 50 \: \text{Hz}$. Attempt The impulse ...
0 votes
1 answer
18 views

How to generate minimum phase convolutions from Z-space sampling?

As far as I understand it, a convolution is classified as minimum phase if and only if all zeroes and poles from its transfer function lie in the Z-plane unit circle. However, I'm having trouble going ...
29 votes
2 answers
20k views

Overlap-Add versus Overlap-Save

What differences or other criteria can be used to help decide between using overlap-add and overlap-save for filtering? Both overlap-add and overlap-save are described as algorithms for doing FFT ...
0 votes
4 answers
142 views

Why do the lengths of the sampled signals $x_1, \: x_2$ have to be $\text{length}(x_1)+\text{length}(x_2)-1$?

We know that convolution in time is equivalent to multiplication in frequency (Fourier). $$x_1(t) \ast x_2(t) \leftrightarrow X_1(\omega)X_2(\omega) \tag1$$ However, for a sampled signal, this ...
2 votes
1 answer
31 views

How do I generate invertible causal filters with stable deconvolution?

I'm writing a machine learning algorithm that needs to search in the space of all possible causal and invertible convolutions/filters of size $k$ represented with floating point precision for one that ...
2 votes
1 answer
251 views

Can time aliasing cause peaks?

For the following I use the terms “time domain signal” and “frequency domain signal” as a Fourier Transform pair. The question is for generalized cases of continuous-time signals that once sampled in ...
4 votes
1 answer
223 views

A new window for the sinc filter and its modifications

There is a recent paper in a journal called ACS Measurements which suggests an alternative window for the sinc function (Why and How Savitzky–Golay Filters Should Be Replaced) Link: Open Access Paper. ...
1 vote
1 answer
149 views

Convolve sinc trains

$$ \begin{align} & \mathrm{sinc}(As + .5)\sum_{n=-\infty}^{\infty} \delta (s - n/A)\ \star \\ & \mathrm{sinc}(Bs + .5)\sum_{n=-\infty}^{\infty} \delta (s - n/B) \end{align} $$ How to compute? ...
2 votes
4 answers
4k 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 ...
0 votes
1 answer
27 views

Comparing two sequences of events for similarity

Suppose I have two sequences of unequal lengths whose elements are timestamps of discrete events in milliseconds: $S_1 = \{150, 200, 700, 1300, 2500\}$, $S_2 = \{300, 670, 900, 1300\}$. These ...
0 votes
1 answer
41 views

Convolution with the Inverse FFT of a Box Filter

I read through this post here on an example of filtering using the box function in fourier space. The example makes sense and I was able to follow it and implement it in Julia (I did in space instead ...
0 votes
1 answer
68 views

How do I properly compute a convolution kernel given the convolved and initial signal?

I'm trying to for solve for $ b $ in the equation $C = a*b$ where $C,a,b$ are 1D arrays of size $k$. $F(b)$ is also $= \frac{1}{|F(a)|}$. I have tried doing the following procedure in order to isolate ...
2 votes
1 answer
102 views

Convolution with Kronecker delta

I know that convolution with delta shifts a signal. As for example, $x \!\left[ n \right] * \delta \!\left[ n - 2 \right] = x \!\left[ n - 2 \right]$. How to do convolution with $x \!\left[ -n \right]$...
0 votes
0 answers
40 views

Is there a computable operation that minimizes entropy?

I have recently experimentally learned that decorrelation does not necessarily imply good compression, but good compressions have the effect of data decorrelation. Since I cannot use autocorrelation ...
1 vote
1 answer
3k views

Convolution in frequency domain, what is the output bandwidth

If two signals do convolution in frequency domain, would the output width/BW be related to the width/BW input signals? Would it be addition or any other?
1 vote
1 answer
99 views

How To Calculate Length Of Sequences And A Suitable N?

I have been struggling to understand how to calculate the length of a sequence and also the minimal N to choose in order to avoid aliasing. Most sources tell me to take the (last non-zero value - ...
1 vote
2 answers
117 views

Linear convolution of a 100 sample time series and a 20 tap filter in the frequency domain

I came across this question on an internship application. For context, I'm three years into my bachelor's for electrical engineering right now. I have learned continuous and discreet convolutions, so ...
14 votes
4 answers
30k views

Why is circular convolution used in DSP? Why not linear convolution?

Why are we using circular convolution in DSP? What's the main solid reason for the use of it in digital processing? Why does the concept of circular convolution come more often than linear ...
5 votes
2 answers
2k views

Show Equivalence Between Multiplication in Time Domain to Convolution in Frequency Domain

My goal is to compute the Fourier of the product between two discrete time signals, y1 and y2. This can be done by computing the ...
1 vote
2 answers
155 views

Why i am not getting same convolution plots?

I am trying to implement convolution using fourier transform property but i am not getting exactly same shape of output that i get by using conv command First portion of graph obtained using conv ...
2 votes
1 answer
71 views

Confusion over deconvolution cost function gradient

A basic deconvolution problem is defined by the cost function $C(f) = ||f \star h - g||^2_2$, where $f$ and $g$ are unknown latent and measured images, $h$ is known kernel. I want to derive the ...
0 votes
1 answer
91 views

realistic sampling - where am I wrong?

I’m given a signal $x(t)$, it's convolved with $h(t)$ and sampled at rate T=1. The result is called $\tilde{x}[n]$. For $$h(t) = \begin{cases} 1 & -0.5<t\le 0.5 \\ 0 & \text{else} \end{...
1 vote
2 answers
114 views

Truncating the output of a digital filter. Which part to discard?

Suppose I have a signal $\mathbf{x}\in \mathbb{C}^{N}$ and a digital filter with impulse response $\mathbf{h}\in\mathbb{C}^L$, where $L<N$. If we pass the signal through the filter, the output will ...
0 votes
0 answers
21 views

Discontinuous functions convolution

Suppose we have these function: I am trying to find their convolution.Since they are both discontinuous when you use the sliding window technique to find the convolution , depending on where t is the ...
1 vote
1 answer
104 views

computing convolution via zero, Periodic padding and FFT - confused about pad length and infinite signals

I’m trying to understand the answer to a test question. The question defines a new transformation for a discrete signal $x[n]$ which is defined for $0 \le n \le N-1$: $$X^c[k] = \sum_{n=0}^{N-1} x[n] ...
0 votes
1 answer
38 views

Morlet wavelet convolution

I use a simple formula (without normalization) from Mike Cohen's "Analzying neural time series data" book. \begin{align} \psi \left( t \right) &= e^{-\frac{t^2}{2 s^2}} \cdot e^{2 \...
2 votes
1 answer
32 views

Derive the filter mask that corresponds to the double filtering process

There are two mask filters, ...
0 votes
1 answer
72 views

Non-uniformly partitioned convolution in real time

I am implementing a real-time convolution reverb. I currently have a working implementation, doing frequency-domain multiplication after FFT, using uniformly partitioned block sizes. This answer on ...
0 votes
1 answer
89 views

Implementing point-wise multiplication as a convolution

As the title says, I'm looking for a way to implement the point-wise multiplication of 2 signals somehow as a convolution. Here's why: In my system, I have an input signal $x[n]$ which has been ...
1 vote
1 answer
239 views

3D convolution product with Fourier transforms, FFTW and MPI in C

My question is not really from the field of signal processing but I think you are the most suited for answering my question. I am willing to compute the gravitational potential which can be written as ...
1 vote
1 answer
77 views

Locate No Signal Area Between 2 Signals

I have many datasets which all looks roughly like this: All the datasets have this in common. First there is an artifact around 0 with an unknown (but likely very high) intensity. Then there is some ...
0 votes
1 answer
43 views

How to make the FIR convolution sum more efficient for continuously filtered signal?

So I want to continuously filter a signal with a causal FIR filter $h$ such that at every sample timestep, I add a new sample to my current set of samples and remove the oldest sample in that set and ...
4 votes
1 answer
349 views

Reduce Signal Size to Compare Them

I have multiple experiments and each of them produce several ($k$ for example) binary signals; some artificial example next: I have a metric to compare experiment results but I need vectors of equal ...
2 votes
2 answers
165 views

Deconvolution with unknown impulse response

This is not a duplicate of Filter secondary bounces of a pulse signal because in that question, a convolution model is finally not appropriate, whereas here, the question is about convolution. Given ...
1 vote
2 answers
122 views

Filter secondary bounces of a pulse signal

I have a single "pulse" signal (looks like a gaussian but it is not exactly), followed by several bounces, with a constant period, that probably come from the electronics used (I don't have ...
2 votes
1 answer
337 views

Proof for the energy correction factor of DFT

I am looking for a mathematical proof for the energy correction factor in conteext of windowed discrete fourier transform. In Spectrum and spectral density estimation by the Discrete Fourier transform ...
0 votes
1 answer
93 views

Why is my Hard Decision Decoding of Convolutional codes not performing well?

I am encoding and decoding a randomly generated bitstream of data using a [5 7] convolutional code. For the decoding part I am using a Viterbi Decoder and trying both HDD and SDD. However, my results ...
0 votes
1 answer
68 views

Correlation between two signals

I am having an input signal x[n]=[1 2 3 4 5 6] and another signal y[n]=[2 3 4]. In order to check whether y[n] is present in the signal x[n],I did cross correlation and the result obtained was [ 0 0 0 ...
9 votes
5 answers
5k 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 ...
2 votes
1 answer
107 views

Correlation gives contradictory results

I am trying to find the correlation between the signals $u(t)$ and $\sin(t)[u(t)-u(t-2)]$ The correlation function $C(t) = \int^{\infty}_{-\infty} u(\tau+t)\sin(t)(u(t)-u(t-2))d\tau$ This is my ...
1 vote
1 answer
61 views

What are the theoretical maximum values of the complex bins in an unscaled FFT of size N?

I am using FFTs to perform real-time convolution of audio signals on small embedded microcontrollers. I am thinking about testing different/smaller data types to represent the complex bins. I am ...
2 votes
1 answer
52 views

2d convolution: What is the difference between convolution using blocked Toeplitz matrix and convolution layers?

For a given matrices $A$ of size $4\times 4$ and $B$ of size $3\times 3$ then I construct a blocked Toeplitz matrix and perform the convolution. The resulting output is of size $6 \times 6$. I have no ...
6 votes
1 answer
427 views

How to Find the Kernel of the Convolution for Linear Interpolation?

I'm trying to solve the following exercise: Image A was doubled by linear interpolation. The magnification was performed in two stages. In the first stage, add about zero pixel to the image between ...
1 vote
1 answer
157 views

Continuous-time convolution of signals with negative amplitudes

While preparing for a mid-term exam, I encountered negative amplitudes for the first time while convolving two signals. I've already solved the problem, but my result and results from others conflict ...

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