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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16 views

Can digital filters actually unmix 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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67 views

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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28 views

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: \begin{equation} x\left(n\...
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29 views

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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79 views

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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33 views

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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33 views

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 ...
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18 views

Perform 2D convolution on a 2D unit step function

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{...
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54 views

Exponential Swept Sine Distortion

I was able to get passable results on fundamental measurements using and exponential swept sine. Now I am trying to get distortion information from the same measurement but am puzzled by the results. ...
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reconstructing a frequency response function from a factor

I am looking at a stationary monopole source with a frequency of 80 Hz with the driving data $1+0i$. It creates an output $-0.191714-0.786113i$ at a certain point $p$. I calculate the "transfer ...
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Convolution and Cross Correlation Blackbox

Suppose I was handed a blackbox that I know is either a Convolution filter or Cross-Correlation filter, and my job is to find out which it is. My idea is to pretend that it's Cross-Correlation and ...
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Series Sum Operator Properties and Identities

As I was reading my book, I came across the following expression: \begin{equation} \sum _{n=-N}^N\sum _{m=-N}^N \phi \left(n-m\right) \end{equation} Then the book said, if we let $k = n-m$, then: \...
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How Come the Low Pass Filter in Sobel Operator Isn't Normalized?

I am relatively new to the field of computer vision and I have just learnt about the sobel operator. The sobel operator in the x direction is a convolution of the finite difference kernel $[1,0,-1]$ ...
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DCT and Convolution, [1994, Martucci]

I am really trying to digest this paper, but the more I read it again, the more I realize that I never fully understood it. Basically, I am trying to get an example where I can check the similarities ...
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Time-shifting operation post the time-reversal operation when performing convolution

I'm confused with the time-shifting operation post the time-reversal operation when performing convolution. Let's say we were to convolve $x(t)$ and $h(t)$, so I would have the term $x(k)$ and $h(t-k)$...
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Solving for a convolved function inside an integral

I have an imaging system that produces a signal in a pixel, in part, by responding to incident radiance $L(\lambda)$ that passes through a filter with transmission $T(\lambda)$. Lumping all the other ...
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If you would write the frequency-response in terms of projections through inproducts. How would you do it?

While studying for signals and systems I realised that the most intuitive way of understanding Fourier Series for me, was to see it as a projection (through inproducts) of a signal onto the orthogonal ...
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Coefficient weights of Simple Moving Average (SMA) on SMA

A simple moving average (SMA: arithmetic mean) is a low-pass FIR-filter. When you cascade 2 SMA's with a window of length $n$, so when you apply the second SMA on the output of the first SMA, and you ...
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23 views

Twisted convolution - simplifying multiple integral via substitution

I need help with understanding a proof from a paper. Following is the description: Let $$r_{1}(t) = \int \int h_{1}\left(\tau, \nu\right) e^{j 2\pi \nu (t - \tau)} s\left(t - \tau\right) d\tau d\nu$$ ...
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Does it make sense to express a given FT from 0 to 1 as a convolution?

I'm learning about Fourier transform, and was asked whether the following FT can be expressed as a convolution: $$X[k] = \sum\limits_{n=0}^{N=1} x[n]e^{-i\frac{2\pi}{N}kn}$$ There are two things I don'...
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63 views

Sifting Property of Shifted Impulse

In the SE Chemistry forum, someone posted an interesting question on converting a scaled and shifted delta function into Lorentzian by convolution please see "simulating a molecular spectrum"...
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38 views

Possible to get transfer function coefficients from window?

I am hoping to use scipy.signals.filtfilt() to smooth some signals in Python, and wanted to build the filter based on a window like a hanning window or whatever. E....
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214 views

Algorithms to re-spatialize a stereo recording audio signal?

Let's say we have an audio signal stereo recording, made for example with a XY microphone positioning: Which algorithms can be used to "re-spatialize" this recording, i.e. try to virtually &...
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35 views

Determine constant $A$ such that $x[n] = x[n] \star x[n]$

Let $x[n] = A\delta[n] - \frac{\sin(\frac{3n}{2})}{\pi n}$. Determine constant $A$ such that for all $n$ $$x[n] = x[n] \star x[n] \tag{1}$$ I think it's not possible since $(1)$ leads to $$X(e^{j\...
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Comparing mechanical signals with different length

I couldn't find any solution for this that would work for me I'm working in python. I have two similar signals that I can plot Force x Angle. (problem simplified) One plot (angle x force) has length ...
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1answer
66 views

Convolution : Anechoic Speech signal and Impulse response

I am trying to perform convolution in MATLAB of an anechoic speech signal (2.1 s) and a impulse response (20 s) using the following code: ...
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PCA with CNN Tensorflow

I need to improve my model of Convolutional Neural Network (CNN). The goal is to recognize facial expression. I've been using some strategies like dropout for regularization and Adam optimazer, but i ...
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3answers
95 views

Matched filter - do I need to know the signal I am trying to find?

I need to identify a matched filter, and so have gone through the mathematics to do this as listed here https://en.wikipedia.org/wiki/Matched_filter which derives the optimal filter $h$ to apply to a ...
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76 views

Laplacian of Gaussian operator

This might be a silly question. I was reading about the Laplacian of Gaussian (LoG) operator and got confused about the alternative equivelant ways we can make use of it. Let's assume we have a 2D ...
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50 views

Is linear convolution same thing as aperiodic convolution?

I am reading an online article and what i understood from there is that linear convolution is aperiodic Is it right? I have also attached snapshot and higlighted two instances
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Kernel vs impulse response: what's the difference? [duplicate]

I am reading The Scientist and Engineer's Guide to Digital Signal Processing by S.W. Smith. In Chapter 9: Applications of the DFT in the 3rd paragraph he writes "kernel (impulse response)" ...
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Convolution for audio, how to control amplitude? [duplicate]

I am implementation a convolution reverb method for audios array in Python using scipy.signal.convolve. I choose the fft mode, which essentially a product of the ...
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46 views

Mulitplication in Frequency Domain as a Similarity Measure of Audio Clips

I have an audio clip and I copy a 256-point part satarting at 10th second. Then I create a 256-point frame on the original clip. At every itreation, I calculate the DFT of the frame, multiply it with ...
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34 views

How to index output of convolution product

Unfortunately indexing the output of convolution product confuses me. Suppose $x[n]$ is of length $15$ (i.e. $0 <= n <= 14$) and $y[n]$ has the length of $9$ ($0 <= n <= 8$). if $z[n]$ be ...
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39 views

Implemenation of Length N Moving average filter using block covolution algorithm(overlap and save algorithm)

I want to implement a Length N moving average filter using block convolution algorithm(overlap save algorithm) I am copying block convolution algorithm(overlap save algorithm) from Proakis, DSP using ...
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40 views

Confusion regarding notation/symbol?

I was reading circular convolution topic from Digital Signal Processing Using Matlab 3rd Ed,by Proakis. I came across a strange term/symbol; I have highlighted it in attached snapshot I have also ...
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55 views

calculate fft convolution for an LTI system given its input (in time domain) and its poles and zeros

I have considered taking the fft (MatLab) of the input (x) and create frequency bins for the first half (problems with an odd number of samples, tried solution zero paddings) and evaluate the transfer ...
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39 views

Confusion regarding plot of linear convolution vs fast convolution via FFT

I am reading Proakis Digital signal processing using Matlab, 3rd edition I am performing example 5.23 but i am not getting same plot/results as book although i am using almost same code First i am ...
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Fast convolution applicable;only circular or also linear/standard convolution?

Fast convolution is the convolution performed using fft Does fast convolution only works for circular convolution or also works for linear/standard convolution?
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39 views

Convolution that outputs a unit impulse

Im thinking whether any convolutional operation can output a unit impulse, an example to further explain: where a convolution between system $h[n]$ and unknown system $g[n]$ would output $\delta[n]$. ...
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1answer
20 views

Time invariance from convolution integral

I wanted to prove, time invariance property of system by convolution integral(i.e equal time shift in input result in equal shift in output) but as calculation shown in figure, I got unexpected result,...
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21 views

Does it make sense to apply convolution in the frequency dimension of a fourier transformed signal?

What I have is more likely a theoretical question. Since I am not from a signal processing background it is hard for me to grasp the issue in using convolution in the frequency dimension of a Fourier ...
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1answer
18 views

Bilinear Interpolation on A Subsection Of An Image

Is it possible to do bilinear interpolation on each 8 by 8 block of an image one at a time until you cover the entire image rather than doing it on the entire image? What are the consequences of this?
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23 views

What happens when you wrap a 3x3 kernel at the corners of an image?

I am puzzled by what actually happens when you process border cases when applying an image filter. For instance if I apply a 3x3 Gaussian kernel to the top left pixel[0][0], the remaining pixels that ...
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2answers
67 views

Proof of fourier transformation of multiplication of two signals

I've been trying to find a proof of the following, but still I m unable to proof it, can someone help me? $$ ℱ[x(t)g(t)] = \frac{1}{2\pi} [X(\omega)*G(\omega)] $$
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59 views

Response of a system using DFT

Let's say that we have two sequences, input sequence $x(n) = [0121]$ and impulse response of a given system $h(n) = [0, 1, -1, 1]$. I need to find response of this system to given input sequence. ...
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45 views

Finding the system output by convolution

pretty new to this concept, so do bear with me. A linear dynamic system is described by the following differential equation: Transfer function H(s) is calculated to be = I've already found the ...
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1answer
32 views

Image Processing [closed]

I have an image and I am trying to find its rows and columns. A = imread('lena.jpg'); nrows = size(A,1) ncols = size(A,2) This is 3 dimensional matrix. Output ...

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