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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Efficient Convolution Without I/O Delay (Gardner 1995) implementation
I am trying to perform real-time convolution on an audio stream using a fairly large FIR for convolutional reverb.
I found a great paper explaining how to do just that: Gardner, 1995. But, I'm new to ...
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Filter design to realize Cauchy product
I come from Computer Science so please pardon for my possibly wrong terminology.
I need to design a filter which has coefficients
$$h_0, h_1, \ldots, h_n, \ldots \quad\text{such that}\quad h_0 > ...
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Analytical Expression for Convolution of Two 2D DFTs
I am trying to do an image analysis problem on some images, and I want to calculate some things in the frequency domain which are giving me problems. Say I have an (discrete) image $I(x,y)$ of size $...
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Blind 1D equalization/deconvolution with some knowledge of filter kernel
Let $s_{\rm out}[n]$ be the 1D output signal of a system, $s[n]$ be the input, and $k[n,q]$ be the filter kernel for an element $n$ and for fixed value $q$. Then:
$s_{\rm out}[n] = s[n] \ast k[n,q]$
...
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Gradient algorithm for Convolutional Blind Source Separation
I'm trying to implement an algorithm for Convolutional Blind Source Separation (CBSS) based on the ALS algorithm for common BSS on this paper.
On this paper, the problem is formulated by (noise ...
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4
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How to Find the Kernel of the Convolution for Linear Interpolation?
I'm trying to solve the following exercise:
Image A was doubled by linear interpolation. The magnification was performed in two stages. In the first stage, add about zero pixel to the image between ...
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107
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Eigenvalues of a product of matrices with specific structures
I'm working on a multichannel feedback system with open-loop frequency response $\mathbf{A}(\omega) = \mathbf{B}(\omega)(\mathbf{C}(\omega)-\mathbf{D}(\omega))$.
The time-domain convolution matrices ...
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4
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Reduce Signal Size to Compare Them
I have multiple experiments and each of them produce several ($k$ for example) binary signals; some artificial example next:
I have a metric to compare experiment results but I need vectors of equal ...
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4
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109
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log(conv) vs conv(log)
Suppose an arbitrary, strictly positive $x[n]$, transformed as
$$
x_l[n] = \log(1 + C x[n]) \tag{0}
$$
where $C$ is freely chosen. Given the following, where $h[n]$ is a Gaussian lowpass filter (or ...
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Nuclear norm minimization of convolution matrix (circular matrix) with fast Fourier transform
I am reading a paper Recovery of Future Data via Convolution Nuclear Norm Minimization. Here, I know there is a definition for convolution matrix.
Given any vector $\boldsymbol{x}=(x_1,x_2,\ldots,x_n)^...
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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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3
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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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Understanding convolution of Chirp z algorithm
I dont´t understand how works the convolution part of the Chirp z.
I understand how the DFT is transformed
\begin{align*}
x(k) = \sum_{n=0}^{N-1} x(n) W_N^{kn}
\end{align*}
to this expresion:
\...
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Convolution of signals sampled on a logarithmic grid
Is there a practical accelerated algorithm or a theoretical discrete (Fourier) transform based method to convolve discrete-time signals sampled on a logarithmic grid? What I mean is representing a ...
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Implementing blind deconvolution in MATLAB
I want to implement blind deconvolution for the signal $ r(n) = h(n) \star s(n) + a(n)$ in MATLAB where
$r(n)$ is the recorded speech
$h(n)$ is impulse response of room acoustics
$s(n)$ is desired ...
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3
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Wavelet computation with filter bank - differing results
I'm trying to get a grip on Wavelets. I've read "Wavelets, Their Friends, and What They Can Do for You" which lead me to an implementation of the discrete DWT with filter banks. Basically, I'm using ...
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1
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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(...
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1
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Proof for the energy correction factor of DFT
I am looking for a mathematical proof for the energy correction factor in conteext of windowed discrete fourier transform.
In Spectrum and spectral density estimation by the Discrete Fourier transform ...
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1
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Can time aliasing cause peaks?
For the following I use the terms “time domain signal” and “frequency domain signal” as a Fourier Transform pair. The question is for generalized cases of continuous-time signals that once sampled in ...
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How can I find the following convolution sum?
$$ h[n]= \left( \frac{8}{9} \right) ^n u[n-3] $$
And the function is:
$$x[n] =
\begin{cases}
2 & \text{if } 0 \leq n \leq9, \\ ...
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Convolve sinc trains
$$
\begin{align}
& \mathrm{sinc}(As + .5)\sum_{n=-\infty}^{\infty} \delta (s - n/A)\ \star \\
& \mathrm{sinc}(Bs + .5)\sum_{n=-\infty}^{\infty} \delta (s - n/B)
\end{align}
$$
How to compute?
...
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Ideal low pass filter with cut-off B does not affect a band-limited baseband signal with maximum frequency B
Let $x(t)$ be a band-limited signal with spectrum (fourier transform) lying between -B and +B. Such a signal is not warped by an ideal low-pass filter with cut-off frequency equal or higher than +B.
...
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2
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Frequency Interpolation of DFT to create Zero-Padded IFFT
As a response to this question I have proposed interpolating new samples in a DFT (meaning the frequency samples of an existing DFT result) sufficient to be the new samples that if we were to take the ...
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2
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Multiple 1D gaussian filter
Given
$$
\begin{cases}
&f_0(x)=1 \\
&f_{n+1}(x)= (\varphi*(f\mathbb{I}_{[a_n,b_n]}))(x)=\int_{-\infty}^{+\infty}\varphi(x-t)f_n(t)\mathbb{I}_{[a_n,b_n]}(t)dt = \int_{a_n}^{b_n}\varphi(x-t)f_n(...
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Combining signals in MFCC space
I'm looking at a data augmentation method for training up a neural network of speech data. Currently I have two version of augmentation.
The first method works by taking an audio file and mixing in a ...
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Showing that filtering a signal with bandwidth B with a brickwall filter of bandwidth W>B has no effect in time domain
The time-domain representation of $G(f) H(f)$, where $H(f)$ is an ideal brickwall filter of bandwidth $1/(2T)$ is:
$$
\int g(\tau) \operatorname{sinc}\left(\frac{t-\tau}{T}\right) d\tau
$$
I want to ...
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Determining the right order of time-domain low pass filter for desired cutoff frequency
I've been stuck on a problem regarding complex demodulation of a signal for a while and wondered if anyone could help.
Suppose I have a signal $X(t)$ such that
\begin{align}
X(t) &= A(t)\cos(\...
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DCT and Convolution, [1994, Martucci]
I am really trying to digest this paper, but the more I read it again, the more I realize that I never fully understood it.
Basically, I am trying to get an example where I can check the similarities ...
- 353
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78
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Solving nonlinear Fourier relation
I'm trying to solve the following nonlinear cross-correlation problem for the time-domain signal $f(t)$:
$S(\omega) = \overline{\mathcal{F}\left[f(t)\right]} \mathcal{F}\left[f^n(t)\right]$
with $n&...
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Gaussian filter convolution giving unexpected results
I am trying to smooth a time series signal with a Gaussian filter and then differentiate the signal (this is for an application for edge detection). A nice property of convolution is:
$$
\frac{d}{dx} \...
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2
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discrete fourier transform circular symmetry
I was reading digital signal processing. In topic Discrete Fourier Transform, circular symmetry it is said that circular advance is obtained by shifting x(n) in clockwise direction. i.e. to obtain x(n+...
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maching convolution filters to results
I am practicing for an exam and I need help in the following question (it is just for me- no grade...)
we get an input image, 6 convolution filters and 6 results.
we need to find the matches between ...
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Convolving two complex signals - relationship between phase
Suppose two continuous complex domain signals are convolved, how is the magnitude and phase of the resultant signal related to the magnitudes and phase of the original signals?
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Deconvolution of non-stationary, 1-D signal?
I have a time series that has been measured after convolution with a moving average filter. Knowing the parameters of the moving average filter, is it possible to reconstruct/constrain the values of ...
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2
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1
answer
441
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How do I pick an optimal window size for overlap add/save method algorithmically
Currently I've implemented an overlap-add method using resources on the internet, but I couldn't find a well documented way to minimize the cost of the method. In other words, how do I pick the window ...
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vote
0
answers
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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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0
answers
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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 ...
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0
answers
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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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1
vote
1
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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 ...
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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 ...
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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 ...
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1
vote
1
answer
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3D convolution product with Fourier transforms, FFTW and MPI in C
My question is not really from the field of signal processing but I think you are the most suited for answering my question.
I am willing to compute the gravitational potential which can be written as ...
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vote
0
answers
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Deconvolution of a ground-penetrating radar signal for further convolution with a desired source signal
I am following the instructions of this paper (https://www.earthdoc.org/content/journals/10.3997/1873-0604.2003015) to process a ground-penetrating radar (GPR) signal (a discrete signal sampled at a ...
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1
answer
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How to perform an analytical computation of the convolution sum for a discrete-time system?
I am trying to follow some notes on "Analytical Computation of the Convolution Sum (Graphical Method)" but am getting stuck on what I am doing, or if what I am doing is correct.
There are 5 ...
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Combining audio and image filters in matlab
I am trying to write audio and image filtering together code in my project.
Purpose: The main aim of this project is to combine audio with image filters; like for example passing low frequencies of an ...
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vote
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Convolution of infinite sums
We have
$$
\sum_{n=-\infty}^{\infty}f(n) \sum_{m=-\infty}^{\infty}g(m) =
\sum_{n=-\infty}^{\infty} \sum_{m=-\infty}^{\infty}g(m) f(n)
$$
and
$$
\int_{-\infty}^{\infty}f(x) dx \int_{-\infty}^{\infty}g(...
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vote
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Labels in speaker verification
I'm a beginner.
If I am using a Convolutional Neural Networks with Triplet Loss as a loss function (also combined with GAN and a Classifier) for building a model that performs Speaker Verification, ...
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vote
0
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What is the Fourier convolution theorem range of application (example of Dirac comb times rectangular window)?
$\DeclareMathOperator{\sinc}{sinc}$
I have questions regarding the Fourier transform of the product of functions or distributions and the range of application of the convolution theorem.
Context
When ...
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1
vote
0
answers
87
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Convolution between a vector and another symmetric vector
Let's have the vector $y = h * x$ where $*$ is the convolution operation, $h$ is the channel with length $N$ and $x$ is a symmetry vector which means $x = [x_M, x_{M-1}, ....,x_0, 0 , x_0, x_1, .... ...
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1
vote
0
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Prove that the twisted Convolution of $f$ and $g$ lies in $L^2(C^n)$?
Edit,this is the exact phrasing of my question
Let $\lambda\in\mathbb{R^n}$.Prove that
$f\star_{\lambda}g\in L^2(\mathbb{C^n})$ for all functions $f$ and $g$
in $L^2(\mathbb{C^n})$.What Happens when $...
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