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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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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 ...
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Bandwidth of convolution of signals [closed]

We have a signal $f(t)$ with a bandwidth of [-300,300] kHz and a signal $x(t)$ with [-400,400] kHz. What is the minimum sampling frequency for the signal $x(t) \star f(t)$ that enables its ...
iasonas's user avatar
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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 ...
Ashik Islam's user avatar
2 votes
1 answer
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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 ...
baronett's user avatar
2 votes
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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 $x \!\left[ -n \right]$...
Nakib's user avatar
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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 ...
Root Groves's user avatar
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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 \...
Rolandos's user avatar
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Derive the filter mask that corresponds to the double filtering process

There are two mask filters, ...
Ryan's user avatar
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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{...
Piratemetaldrinkingcrew's user avatar
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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] ...
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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 ...
Quéston Questioneer Esquerie's user avatar
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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 ...
g6kxjv1ozn's user avatar
1 vote
2 answers
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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 ...
DSP_CS's user avatar
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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 ...
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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 ...
Sherlock Rozman's user avatar
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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 ...
Dani S.'s user avatar
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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 ...
Aami's user avatar
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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 ...
Tobias Hienzsch's user avatar
1 vote
1 answer
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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 - ...
Sugi's user avatar
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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 ...
kesetovic's user avatar
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Use DFT (`fft()`) to Replicate 2D Convolution (`conv()`)

In MATLAB, I tried to convert the fft2-based multiplication using conv2. ...
Ka Mirul's user avatar
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1 answer
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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 ...
Sammy Apsel's user avatar
2 votes
1 answer
119 views

What is the rationale behind the "same" mode of discrete convolution?

Having read up on discrete convolution and how it is implemented, I've started to think about which "mode" is applicable to which situation. For two signals ...
Doddy's user avatar
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Filtering in time domain vs filtering in frequency domain

The signal is an impulse repsonse. I am filtering the signal using a windowed sinc filter in both frequency and time domain. I am interested in knowing the differences between the two methods and ...
Tanmayee Pathre's user avatar
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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 ...
Math_Novice's user avatar
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Determine Noise Level by Convolving N Signals

I using a microphone to determine (air) leakage characteristics. The signals need to be filtered to reduce the noise level and i thought of using the Spectral Subtraction Technique. Since im having 4 ...
Tom's user avatar
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Fourier transform of $|x_\mathrm{a}(t)|^2$

Let $x_\mathrm{a}(t)$ be the analytic signal for real signal $x(t)$. I want to find an expression for $\mathscr{F}\{|x_\mathrm{a}(t)|^2\}(f)$ in terms of $x(t)$. The analytic signal can be written as $...
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Does block-based FIR filtering necessarily imply using the DFT?

Assume I want to filter a stream of data with a rather small FIR filter (in the order of 16 to 64 coefficients). In any case I have to split the input stream into chunks (blocks) of data. Searching ...
Junius's user avatar
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Infinite Sum of Future Signal Values of an LTI System

Let $x[n]$ be the input and $y[n]$ be the output of an LTI system. That is, $y[n]=\displaystyle\sum_{k=-\infty}^{\infty} h[n-k]\space x[k]$ where $h[\cdot]$ is the impulse response function. We are ...
singular's user avatar
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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(...
singular's user avatar
2 votes
1 answer
204 views

What is the Fourier Transform of $\operatorname{sgn}(t) \cdot \operatorname{sgn}(t)$?

I am wondering what the Fourier Transform of $\operatorname{sgn}(t) \cdot \operatorname{sgn}(t)$ will be, where $\operatorname{sgn}(t)$ indicates the signum function. It would seem obvious that this ...
Finn Heijink's user avatar
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1 answer
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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 ...
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Why are convolutions between those functions equivalent (signal processing for theoretical neuroscience)?

I'm reading a book on theoretical neuroscience [1], in which the following definitions are given: $\rho(t)=\sum_{i=1}^n \delta(t-t_i)$ where $\delta$ is Dirac's delta and the $t_i$ are timestamps at ...
Ash's user avatar
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Convolution output signal transient correction

I'm just starting out in signal analysis and I've come across this effect. When I use convolution of a sinusoid with any other, either triangular pulse, rectangular pulse or decreasing exponential (...
diegobrsrk's user avatar
1 vote
1 answer
271 views

Proving that the autocorrelation of a signal is the convolution with its time-reversed complex conjugate

I need to prove the property $$f(x)⊕f(x)=f(x)⊗f^*(-x)$$ That is the autocorrelation of a function is the convolution with its time-reversed complex conjugate. I have constructed most of the proof but ...
requiemman's user avatar
2 votes
1 answer
234 views

Impulse Response for an Input-Output Pair

Given an input-output pair of a LTI system \begin{gather*} x[ n] \ =\ 2\delta [ n+2] -\delta [ n+1] +\delta [ n-1]\\ y[ n] \ =\ 4 \delta [ n+2] +\ 4\delta [ n+1] -\delta [ n-1] \end{gather*} My ...
Anmoldeep's user avatar
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Equipment to test my theory on time varying systems

How can I make a linearly time varying system to test my theory? Can I ask for a PID microcontroller available from my university such that $K$ is gradually increased from 0 to $c$
Volpina's user avatar
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Fusing convolutions

I am attempting to combine two consecutive 2D convolutions into a single 2D convolution. Ideally, a convolution operation is a linear transformation, so it should be possible to merge two linear ...
Federico Fontana's user avatar
1 vote
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52 views

PyWavelets CWT : error when differentiating after convolution?

I'm trying to understand the implementation of CWT in PYWT. This topic has already helped me quite a lot but there is still a thing that is unclear to me : why is the result differentiated only after ...
Tanguy Jonv's user avatar
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1 answer
77 views

How would the correlation coefficient between 2 images change if we rotated 1 image?

Suppose we have a image which is represented by a matrix $ \begin{bmatrix} a & b & c \\ d & e & f \\ g & h & i \\ \end{bmatrix} $ and we want to find its correlation with ...
Cerise's user avatar
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Having problems with convolution in Fourier space

First attempt: I tried convolution in Fourier space. step: transform grayscale image ==> (real1,imag1) step: transform kernel (a simple box filter) ==> (real2, imag2) step: multiply (complex) ==...
Gianni's user avatar
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Why will the output be imprinted with delay effect or echo after convolving two direct dry signals' FFT values (convolution filtering)

I am recently working on the reproduction of the filtering effect of target play back devices, like phone, or speakers, etc using convolution techniques in MATLAB. I firstly created a function called &...
CPK's user avatar
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2 votes
1 answer
105 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 ...
Cerise's user avatar
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1 answer
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How to handle undefined functions in a convolution?

When convolving with undefined functions, do we just treat them like variables? (eg. How do I handle $u \left( k \right)$ and $u \left( n - k \right)$ since they are just step functions with no ...
Axel's user avatar
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Incorrect Power Calculation in MATLAB Convolution

I have been working on a MATLAB code to perform convolution and calculate the power of the resulting signal. However, I have encountered an issue with the power calculation in my code. I am convolving ...
Marcus's user avatar
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1 vote
2 answers
361 views

Why does convolution give the output of a passing a signal through a filter?

I have a rudimentary understanding of Convolution, the Convolution Theorem and why the output z(t) of an LTI system can be found using the convolution of input signal x(t) and the impulse response h(t)...
SNIreaPER's user avatar
1 vote
1 answer
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Why is the convolution of two sine waves a sinc function?

Problem/Question After taking the convolution of two discrete sine waves of the same frequency and length the result appears to be a sinc function but I was expecting to get a sine wave since this ...
Usman Mutawakil's user avatar
1 vote
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Doubt on linear and circular convolution derivation

[I'm very new to this website and to DSP in general as well! :)] Hello everyone! I have a question on the derivation of the circular convolution. As far as I understand, we can define a circular ...
edoverg's user avatar
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Is flipping a vector x the same as x[-n]?

I was intending to use the following convolution property in my Matlab code. $$y[-n]=x[-n]*h[n]=x[n]*h[-n]$$ However, I am noticing that the results seems not the expected ones, for example let have <...
ndarkness's user avatar
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Inequality involving zero-crossings of Difference of Gaussian and Laplacian of Gaussian

I am stuck on the following problem: Let $f$ be a smooth real function with a single inflection point and let $\sigma_1>\sigma_2>0$ be two real numbers. We denote $G_1$ and $G_2$ the associated ...
NancyBoy's user avatar
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