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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Linear Phase Filters and FFT

The FFT decomposes a signal into cosine and sine functions, respectively, even and odd components of the signal. Hence, I would expect even symmetric filters to have zero imaginary parts. Suppose a ...
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1answer
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Identify out signal from in signal and impulse response

Hi there I am studying a course in signal processing and systems. I was given an excecise which I am having a great deal of trouble solving. I am allowed to solved using matlab, but for top marks I ...
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real time - active noise control

I am trying to implement an adaptive filter for system identification and active noise control for realtime signal processing on an FPGA using Labview. For system identification, I implemented the ...
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1answer
52 views

How to compute convolution using the Discrete Hartley Transform

It's easy to compute the Discrete Hartley Transform of a 1D signal: ...
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1answer
48 views

signals and systems,matched filter concept

The system with impulse response hi(t) is known as the matched filter for the signal Xi(t) because the impulse response is tuned to xi(t) in order to produce the maximum output signal. My intuition ...
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2answers
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Deconvolution of system response in Python/Matlab

I had two sets of data, the output function of the system (time series with a length of 1292 entries) and the transfer function (similar to a gaussian with a length of 681 entries). I would like to ...
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how to get N point FIR filter( convolution) output when input and impulse response are both N points ? ideally convolution results in length N+N-1

x[n] -> Input Signal of length N h[n] -> Impulse response of length N y[n] = x[n]*h[n] (convolution to get the output of this FIR filter) Ideally length of y[n] should be N+N-1 but is it ...
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Convolving a LP FIR filter with a HP FIR filter

I currently feed a sampled audio input signal into a 511 tap highpass FIR filter, the output of which is then fed to another 511 tap lowpass FIR filter, resulting in a very narrow bandpass filter ...
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2answers
51 views

Energy-preserving convolution kernel?

Is there a function, in continuous or (primarily) discrete time, such that convolving with it preserves the input's energy? For $x$ that is finite-valued, finitely supported in time, and: Real or ...
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Moving average filter using DF-I and DF-II

I understand that the moving average filter is simply the average of a number of points from the input signal to produce the output signal. If x[] is the input and y[] is the output and M is the ...
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2answers
31 views

Deconvolution of shifted gaussian function in the frequency range

I have a signal defined as $$A(t)\cdot\exp\left(-i\omega_0t\right)$$ with $A$ the envelope function and $\omega_0$ the carrier frequency. I would like to transfer this signal into the fourier space ...
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1answer
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Replicate MATLAB's `conv2()` in Frequency Domain

When conv2d is on valid mode, the image needs no padding, because the result is the same size as the image. When conv2d is on ...
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FIR Filter design, using different filter length than signal length

Given some neurophysiological application I am filtering in real time data of limited length (e.g. in epochs of 100 ms) using a sampling rate of e.g. 100 Hz. Due to this short time segment I am trying ...
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Convolution Reverb Calculation

Here's my basic understanding of how to implement a convolution reverb: I measure the IR of a space using a sine sweep. The raw mic output is stored as a Voltage-Time data set. Let's assume that this ...
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Boundary effects with scipy.fftconvolve after convolution

I am having some numerical error in my code that propagates continuously, and has to do with the implementation of convolutions in Python; this is kind of struggling my progress and I would really ...
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Equalizing audio under linux / Raspberry Pi

I have an audio streaming receiver written in Python running on a raspberry pi. This receiver writes the streamed audio out to an alsa device, which in turn passes it to an amplifier which is driving ...
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Under what conditions is the convolution of an input signal with the system's impulse response periodic?

I'm currently solving the following convolution problem from Oppenheimer's book: In the solution, it was stated that "$x(t)$ periodic implies $y(t)$ is periodic" So I wondered if it's ...
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Filtering relationship for sources propagating over a sensor array

A sensor array $y$ measures the superposition of $N$ sources $s$, at time $t$ and position $x$ we have : $$y(t,x)=\sum_{i=1}^{N} s_i(t,x)$$ The sources $s$ travel at constant speed over the array of $...
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Calculating cross-correlation using Walsh-Hadamard transform

I am trying to implement MLS method of measuring impulse responses. There is an article describing the method: http://www.commsp.ee.ic.ac.uk/~mrt102/projects/mls.... As I understand, to get an impulse ...
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Physically, what does the usage of two variables mean for convolution

My intuition of convolution is that it is just a way to depict multiplication of two signals where each signal is made up of various frequencies and phases. Since it isn't easy to find the value of $\...
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Image convolution using FFT

I just can't get my head around Fourier transform and convolution in 2D. I am trying to implement image convolution using fast Fourier transform (in julia). So the first thing I need to do is to pad ...
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Combining signals in MFCC space

I'm looking at a data augmentation method for training up a neural network of speech data. Currently I have two version of augmentation. The first method works by taking an audio file and mixing in a ...
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1answer
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bit reversed order of FFT matrix for channel estimation

Although the question seems similar to this one HERE, but what I want to ask about is little bit different. Assume we have a signal $X$ whose length is $N$x$1$, we convert that signal into time ...
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1answer
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Channel estimation using bit reversed order of FFT matrix

Is it possible to use the bit-reverse order of FFT instead of FFT to estimate the channel? Based on my reading, I found that bit reversed order of FFT matrix can diagonalize the channel, but ...
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1answer
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Scaling the input vs scaling the impulse response for an LTI system

Two different cases: We pass $x(t)$ to an LTI system with impulse response $h(2t)$ and get the output $y(t)$. We pass $x(2t)$ to an LTI system with impulse response $h(t)$ and get the output $z(t)$. ...
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Upsampling class activation maps for discriminative feature localisation

I am currently reading a paper by on learning deep features for discriminative localization where the authors propose to use class activation maps to learn discriminative localised features. The ...
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convolution of two exponential signals with imaginary numbers

I can solve problems without imaginary numbers, but when exponential contain imaginary numbers, I can't solve the problem. For example, $x(t)=e^{3jt}+e^{4jt}$, $y(t)=(e^{-3t}-e^{-4t})u(t)$ (where $j$ ...
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Unit impulse response of a cascade interconnection of three discrete-time systems

I am nearly at the end of finishing a problem in my textbook but I couldn't understand something in the answer; I did everything to the point I found the overall response of the system in terms of $...
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Edge artifacts in frequency-domain Moving Average filter

I am currently trying to implement in python an algorithm to identify and filter out one specific periodic EEG artifact -- the grad fMRI artifact -- as described in this paper, and I am incurring in ...
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1answer
43 views

Finding Interval of Integration

If we let : $$ x(t)=\begin{cases} 1&\text{if $0<t<1$}\\ 0&\text{if otherwise} \end{cases} $$ and $$ h(t)=x(t/a)=\begin{cases} 1&\text{if $0<t<a$}\\ 0&\text{if otherwise}\...
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Computing Discrete Convolution in terms of unit step function

Consider : $$ x[n]:=\begin{cases} 1&\text{if $3\leq n\leq 8$}\\ 0&\text{if otherwise} \end{cases} \quad\text{and}\quad h[n]:=\begin{cases} 1&\text{if $4\leq n \leq 15$}\\ 0&\text{if ...
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Confused about shifting convolutions

We know that for two signals $x[n]$ and $h[n]$ such that : $$ y_{1}[n]=(x*h)[n]=\sum_{k=-\infty}^{\infty}x[k]h[n-k]=\sum_{k=-\infty}^{\infty}h[k]x[n-k] $$ We can deduce that :$$y_{2}[n]=x[n+2]*h[n]=y_{...
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What is the best way to spatialise a real-time stream of a speech? Developing a C++ engine

I'm working on a mobile application in C++. The app brings listeners to a virtual room to listen to real-time streams, such as interviews, talks, lectures. The idea is to make sound immersive, to give ...
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1answer
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Determine g(t) for minimal symbol error probability, given h(t), K=1 and Minimum distance receiver

Determine $g(t)$ for minimal symbol error probability, given $h(t)$, $K=1$ and Minimum distance receiver. $h(t)= \begin{cases} 0, & \text{$t<0$}\\ 2, & \text{$t\in(0\;, 10^{-3}...
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58 views

Constructing a Gaussian kernel in the frequency domain

I'm currently learning about Fourier transform, but find the differences between spatial domain and frequency domain a bit confusing at times. Let's say I would like to perform convolution of an image ...
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54 views

Why there is static noise and voice distortion after convolving it with impulse response?

I have been working on the decorrelation of audio signals while following this paper : The Decorrelation of Audio Signals and Its Impact on Spatial Imagery So far I have generated impulse responses in ...
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1answer
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Is the expansion of this expression correct?

\begin{align*} &(\delta[n]+\delta[n-1])*(\delta[n]+\delta[n-1])\\ \\ =\;&\delta[n]*\delta[n]+2(\delta[n]*\delta[n-1])+\delta[n-1]*\delta[n-1]\\ \\ =\;&(\delta[n]+2(\delta[n]*\delta[n-1])+\...
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UPDATE : How to continue Computing the Convolution

$$ x(t):=\begin{cases} 1&\text{if $0<t<T$}\\ \\ 0&\text{if otherwise} \end{cases} \qquad\text{and}\qquad h(t):=\begin{cases} t&\text{if $0<t<2T$}\\ \\ 0&\text{if otherwise} ...
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1answer
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Where is the mistake in the convolution?

Let : $$ x[n]=\begin{cases} 1&\text{if $0\leq n\leq 4$}\\ \\ 0&\text{if otherwise} \end{cases} \qquad \text{and} \qquad h[n]=\begin{cases} \alpha^{n}&\text{if $0\leq n\leq 6$}\\ \\ 0&\...
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1answer
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Discrete Convolution of two piecewise sequences having this specific form

Assume I have the following two sequences : $$ x[n]=\begin{cases} \alpha&\text{if $a\leq n\leq b$}\\ \\ \tag{1} 0&\text{if otherwise} \end{cases} \qquad \text{and} \qquad h[n]=\begin{cases} \...
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1answer
60 views

Finding the impulse response given response to another signal

I was trying to solve this question : I respresented $x(t) = u(t+1)-u(t-1)$ writing the convolution as $[u(t+1)-u(t-1)]*h(t) = y(t)$ I then used the property of differentiation to convert from the ...
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1answer
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Initial rest condition applied on $x(t)$ vs $h(t)$

Define the LTI system $\mathcal{H} : x\mapsto y$ Define the convolution for continuous-time system : $$ (x*h)(t)=\int_{-\infty}^{\infty}x(\tau)h(t-\tau)\;\text{d}\tau $$ The initial rest condition ...
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1answer
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Circular wrapping of an asymmetric function (in DFT calculations)

Convoluting a signal (using discrete FT) for a given interval [a, b] with a Gaussian can be done by circular wrapping as shown in Numerical Recipes. I found a shortcut for circular wrapping so that ...
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1answer
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Convolution of discrete signals using convolution sum

I want to perform the convolution of the following discrete signals: $$h[n]=u[n-2] $$ and $$x[n] = (0.5)^nu[n+2]$$. That's what I've done so far: $$\sum_{k=-\infty}^{\infty} (0.5)^ku[k+2]*u[n-2-k]$$ ...
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Deconvolution of sidelobes in a point spread function?

It seems that most deconvolution algorithms mainly handle the main lobe of a point spread function (PSF) and assume that sidelobes can be safely neglected. For a direct algorithm trying to perform a ...
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1answer
42 views

PID and convolution

In that formula : $$ u(t)=K_{\mathrm{P}} e(t)+K_{\mathrm{I}} \int_{0}^{t} e(\tau) \mathrm{d} \tau+K_{\mathrm{D}} \frac{\mathrm{d} e(t)}{\mathrm{d} t} $$ I know from the formulae collection we refer to ...
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Filter length (N) has no effect on the reconstructed signal & Toeplitz Matrix

Hello Signal Processing community, I implemented a filtering algorithm called Minimal Mean Squared Error in Frequency domain with N-coefficient and Signal Detection (FMSENSD) in MATLAB, I got some ...
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Delay a signal in time vs in frequency

I have a signal h that I want to delay for a time t. I know that I could use two possible approaches: $h_{\text{delay}}[k] = \...
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How do I perform 2D Fourier domain multiplication if the filter mask doesn't match the image size?

Let's say I have an image that is 512 x 512 pixels. I've been tasked with creating two ideal half-band low-pass filters that will filter the image. The first filter is 8 x 8, and the second one is 16 ...
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Feature Based Methods for Quality Inspection Problem

I am currently working on an image classification problem to classify thermal images (can be interpreted as false-color images) of certain products as with or without defect. From an initial search in ...

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