# 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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### 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 ...
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### 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. ...
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### 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 ...
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### 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 ...
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### 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 ...
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### 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 ...
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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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### 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 ...
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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 ...
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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 $x \!\left[ -n \right]$...
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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 ...
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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 \...
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### Derive the filter mask that corresponds to the double filtering process

There are two mask filters, ...
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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 ...
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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 ...
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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 ...
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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 ...
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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 ...
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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 ...
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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 ...
1 vote
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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 - ...
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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 ...
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### Use DFT (fft()) to Replicate 2D Convolution (conv())

In MATLAB, I tried to convert the fft2-based multiplication using conv2. ...
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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 ...
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### 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 ...
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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 ...
1 vote
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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 ...
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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 ...
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### 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 ...
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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 ...
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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 (...
1 vote
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### 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 ...
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### 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 ...
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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 $c$
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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 ...
1 vote
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### 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 ...
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### 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 ...
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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) ==...
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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 &...
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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 ...
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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 ...
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