# 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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### Reconstructing signal from frames

Edit: Please treat code here as python-esque pseudo-code; it would syntactically fall closest to MATLAB or Python+numpy+scipy users. If I have a signal in frames, and I want to put it back together - ...
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### Convolution of two sets

In my systems and signals course I had been asked a question about finding the convolution of two sets. I was given: \begin{align} x[n] &= \{3,2,1\}\\ h[n] &= \{1,-2,3\}\\ \text{Find}\quad ...
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### What is the correct length for obtaining a true linear convolution from DFT?

In the linear convolution of two equal length sequences M and N, the length of the output is length(A)+length(B)-1, and if we apply the DFT property of converting convolution into multiplication, the ...
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### Possibilities in Audio Convolution Math

New Python user here! I am a musician working on a program to streamline a process of using convolution math on a folder of .wav samples. The idea is that each audio sample will be multiplied with ...
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### multiplication of a function with a Fourier-transformed equals to Fourier-transformed with a function

I already showed b item using the fact that it is $h\left(0\right)=\int \:f\left(t\right)g\left(0-t\right)dt$ I struggle a lot of hours trying to find the trick in item C. Can anyone help please ?
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### Inverse system of sinc?

I'm doing some self-study for an important exam I'll have in late March and came across the following question: So, using the convolution properties, if I want to find an identity system so that the ...
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### Concrete use of convolution algebraic properties [closed]

There are 3 main properties of convolution in every image processing lecture notes I read : Commutativity: $f\star h = h\star f$ Associativity: $f\star (h_1\star h_2) = (f\star h_1)\star h_2$ ...
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### Mathematical expression of Multicarrier frequency equalizer

I have a signal $X$ with length of $N$, multiplied with any unitary matrix, i.e the transpose of DCT matrix as: $x = D' X$ where $D'$ is the transpose of the of DCT matrix. Then let's add $CP$ guard ...
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### How to figure out the polynom of Convolutional encoder

I have Convolutional encoder with K=7, r=1/2 that steam of bits get enter to it from right to left (7 registers and steam of input is entering the convolutional encoder from left to right .. ) the ...
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### The impulse response of a LTI discrete system is $h[n]=\big(\frac{1}{3}\big)^n u[n]$. Find the response of this system to the input $x[n]= e^{jnπ/4}$

Hi I'm trying to solve the problem when studying for an upcoming test. The given solution is $1.2503 e^{jnπ/4 -0.2991}$, and is found by computing $H(Ω)$ and evaluating this at $Ω=π/4$. when I try ...
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### Finding the convolution $a^n u[n]$ with $b^n u[n]$

Hi I'm trying to solve the problem when studying for an upcoming test. The given solution is $$y[n]= \frac{1}{b-a}(b^{n+1}-a^{n+1}) \quad \text{for } n\ge0 \ .$$ However, I'm not sure how to reach ...
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### Linear convolution in the DFT domain

Let's say I have 2 sequences a and b in the time domain. Both are length N. A and B are the DFT of a and b. If I do a circular convolution of A and B in freq domain (A o B), then the IDFT of the ...
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### Calculation of eigendecomposition of a signal in its Fourier domain?

I want to find the eigendecomposition of a 3-dimensional discretely sampled signal $X$, where each sample $X_{i,j,k}$ is treated as a vector $\langle i, j, k\rangle$ (with the origin at the middle of ...
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### Unclear time-to-frequency integration step

From here; $\hat f=\mathcal{F}(f)$, bar = complex conjugate: Time-shift property: $x(t-b) \Leftrightarrow e^{-j\omega b}{\bf X} (\omega)$, so why is it $+$ (red)? What at all is happening? Looks like ...
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### PyWavelets CWT: resampling vs recomputing wavelet

Related. The implementation pre-integrates a wavelet once, and resamples it at each scale, finally differencing to implement ...
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### Multiple short-range impulse responses aggregated to simulate a long-distance impulse response

I'm a biologist and I was thinking of ways that impulse responses could be used to simulate how an animal sounds over various distances in different types of forests. Ultimately, if a tool was ...
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### PyWavelets CWT implementation

I seek to understand PyWavelets' implementation of the Continuous Wavelet Transform, and how it compares to the more 'basic' version I've coded and provided here. In particular: How is integrated ...
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### Convolutions with changes to the argument

I think I understand what happens when I shift the argument, but I'm not sure what should happen when the signal is compressed or expanded. In particular I'm trying to figure out what happens when the ...
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### Showing that filtering a signal with bandwidth B with a brickwall filter of bandwidth W>B has no effect in time domain

The time-domain representation of $G(f) H(f)$, where $H(f)$ is an ideal brickwall filter of bandwidth $1/(2T)$ is: $$\int g(\tau) \operatorname{sinc}\left(\frac{t-\tau}{T}\right) d\tau$$ I want to ...
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### Can digital filters actually separate signals?

I've come to realize what appears to be a hard limit in convolution theorem: to avoid time-domain aliasing, we must pad the signal/filter, but the padding distorts the spectrum. Consider a ...
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### Amplitude Matching for Exponential Swept Sine

I am working in the area of aerospace vibration testing and we use swept sine tests on structures and measure the response using the accelerometers. I tried implementing the technique "...
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### Why does time-domain convolution correspond to frequency-domain multiplication? (visual)

I seek a visual explanation of this. I've already seen the maths, and can derive the proofs - they amount to nill for an intuitive understanding. Any amount of math is welcome, as long as serving to ...
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### Channel equalization affect on input signal

I have the following problem. Am trying to understand how the channel block affects the input signal s(n). I know that x(n), the input signal to the filter is basically: x\left(n\...
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### attenuation of the central difference differentiator

In the following snippet, I am differentiating a sine wave using the central difference equation, first through misc.derivative and then through convolution with the kernel [1/2, 0, -1/2] ...
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### Determining the right order of time-domain low pass filter for desired cutoff frequency

I've been stuck on a problem regarding complex demodulation of a signal for a while and wondered if anyone could help. Suppose I have a signal $X(t)$ such that \begin{align} X(t) &= A(t)\cos(\...
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### Fourier Transforms, Convolution, Cross-correlation: what is their physical unit exactly?

Let us assume we are talking about real, deterministic, electrical signals $x(t)$ and $y(t)$ (magnitude in Volts). There are different kind of Fourier Transforms. I made a table to summarize: NB: By ...
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### Convolution of rectangular function with sinc function

I'm trying to create a rectangular function, defined between -0.5 to 0.5 I'm then convoluting it with a sinc function (using numpy.sinc) and plotting the convoluted ...
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### Computing Autocorrelation via FFT

I have seen several methods to calculate Autocorrelations using FFTs, and am confused about why they differ. Zero-Pad it to double its original length.Take the FFT. Then replace all the coefficients ...
I am stuck with the following 2D convolution: Consider the sequence $f$ defined by the following: \$f[m,n] = \begin{cases} 1 & \text{0≤ m ≤ n} \\\ 0 & \text{otherwise}\\ \end{...