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.
165
questions with no upvoted or accepted answers
7
votes
0
answers
443
views
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 ...
- 171
7
votes
1
answer
270
views
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
$$h_0, h_1, \ldots, h_n, \ldots \quad\text{such that}\quad h_0 > ...
7
votes
1
answer
401
views
Analytical Expression for Convolution of Two 2D DFTs
I am trying to do an image analysis problem on some images, and I want to calculate some things in the frequency domain which are giving me problems. Say I have an (discrete) image $I(x,y)$ of size $...
- 171
5
votes
0
answers
365
views
Blind 1D equalization/deconvolution with some knowledge of filter kernel
Let $s_{\rm out}[n]$ be the 1D output signal of a system, $s[n]$ be the input, and $k[n,q]$ be the filter kernel for an element $n$ and for fixed value $q$. Then:
$s_{\rm out}[n] = s[n] \ast k[n,q]$
...
- 963
4
votes
0
answers
78
views
Gradient algorithm for Convolutional Blind Source Separation
I'm trying to implement an algorithm for Convolutional Blind Source Separation (CBSS) based on the ALS algorithm for common BSS on this paper.
On this paper, the problem is formulated by (noise ...
- 137
4
votes
0
answers
109
views
Eigenvalues of a product of matrices with specific structures
I'm working on a multichannel feedback system with open-loop frequency response $\mathbf{A}(\omega) = \mathbf{B}(\omega)(\mathbf{C}(\omega)-\mathbf{D}(\omega))$.
The time-domain convolution matrices ...
- 143
4
votes
1
answer
359
views
Reduce Signal Size to Compare Them
I have multiple experiments and each of them produce several ($k$ for example) binary signals; some artificial example next:
I have a metric to compare experiment results but I need vectors of equal ...
- 41
4
votes
1
answer
110
views
log(conv) vs conv(log)
Suppose an arbitrary, strictly positive $x[n]$, transformed as
$$
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 ...
- 9,054
3
votes
0
answers
89
views
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)^...
- 31
3
votes
0
answers
392
views
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 ...
- 31
3
votes
0
answers
101
views
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:
\...
- 31
3
votes
0
answers
101
views
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 ...
- 13.6k
3
votes
0
answers
525
views
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 ...
- 31
3
votes
0
answers
359
views
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 ...
- 131
2
votes
1
answer
108
views
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]$...
- 21
2
votes
1
answer
61
views
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(...
- 63
2
votes
0
answers
115
views
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, \\ ...
- 1,593
2
votes
0
answers
89
views
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.
...
- 334
2
votes
0
answers
301
views
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 ...
- 53.8k
2
votes
0
answers
166
views
Multiple 1D gaussian filter
Given
$$
\begin{cases}
&f_0(x)=1 \\
&f_{n+1}(x)= (\varphi*(f\mathbb{I}_{[a_n,b_n]}))(x)=\int_{-\infty}^{+\infty}\varphi(x-t)f_n(t)\mathbb{I}_{[a_n,b_n]}(t)dt = \int_{a_n}^{b_n}\varphi(x-t)f_n(...
- 143
2
votes
0
answers
93
views
Combining signals in MFCC space
I'm looking at a data augmentation method for training up a neural network of speech data. Currently I have two version of augmentation.
The first method works by taking an audio file and mixing in a ...
- 475
2
votes
0
answers
52
views
Showing that filtering a signal with bandwidth B with a brickwall filter of bandwidth W>B has no effect in time domain
The time-domain representation of $G(f) H(f)$, where $H(f)$ is an ideal brickwall filter of bandwidth $1/(2T)$ is:
$$
\int g(\tau) \operatorname{sinc}\left(\frac{t-\tau}{T}\right) d\tau
$$
I want to ...
- 473
2
votes
0
answers
470
views
Why does time-domain convolution correspond to frequency-domain multiplication? (visual)
I seek a visual explanation of this. I've already seen the maths, and can derive the proofs - they amount to nill for an intuitive understanding. Any amount of math is welcome, as long as serving to ...
- 9,054
2
votes
0
answers
108
views
Determining the right order of time-domain low pass filter for desired cutoff frequency
I've been stuck on a problem regarding complex demodulation of a signal for a while and wondered if anyone could help.
Suppose I have a signal $X(t)$ such that
\begin{align}
X(t) &= A(t)\cos(\...
- 141
2
votes
0
answers
92
views
DCT and Convolution, [1994, Martucci]
I am really trying to digest this paper, but the more I read it again, the more I realize that I never fully understood it.
Basically, I am trying to get an example where I can check the similarities ...
- 363
2
votes
0
answers
79
views
Solving nonlinear Fourier relation
I'm trying to solve the following nonlinear cross-correlation problem for the time-domain signal $f(t)$:
$S(\omega) = \overline{\mathcal{F}\left[f(t)\right]} \mathcal{F}\left[f^n(t)\right]$
with $n&...
- 121
2
votes
0
answers
244
views
Gaussian filter convolution giving unexpected results
I am trying to smooth a time series signal with a Gaussian filter and then differentiate the signal (this is for an application for edge detection). A nice property of convolution is:
$$
\frac{d}{dx} \...
- 290
2
votes
0
answers
929
views
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+...
- 123
2
votes
0
answers
93
views
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 ...
- 21
2
votes
0
answers
1k
views
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?
- 155
2
votes
0
answers
246
views
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 ...
- 239
2
votes
1
answer
532
views
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 ...
- 121
1
vote
1
answer
113
views
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 - ...
- 11
1
vote
2
answers
130
views
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 ...
- 141
1
vote
0
answers
66
views
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 ...
- 131
1
vote
0
answers
55
views
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
0
answers
56
views
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 ...
- 11
1
vote
0
answers
57
views
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 ...
- 11
1
vote
0
answers
59
views
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 ...
- 11
1
vote
1
answer
253
views
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 ...
1
vote
0
answers
99
views
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 ...
- 33
1
vote
1
answer
344
views
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 ...
- 33
1
vote
0
answers
63
views
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 ...
- 11
1
vote
0
answers
178
views
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
$$
\int_{-\infty}^{\infty}f(x) dx \int_{-\infty}^{\infty}g(...
- 9,054
1
vote
1
answer
154
views
Convolve sinc trains
$$
\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?
...
- 9,054
1
vote
0
answers
85
views
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, ...
- 11
1
vote
0
answers
127
views
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 ...
- 11
1
vote
0
answers
91
views
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, .... ...
- 640
1
vote
0
answers
179
views
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 $...
- 11
1
vote
0
answers
96
views
How to update point spread function of blind deconbolution by conjugate gradient?
There is an unblurred image $g$ and a blurred image $x$.
Their relationship is expressed by the following formula using $psf$(point spread fucntion, size is $5×5$ kernel).
$g = x \otimes psf\tag 1$
...
