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.
2
votes
2answers
38 views
CDMA : Calculating M from m1 * w1, m2*w2, etc M as Walsh Code, M as Orthogonal COde
I have these values,
m2 = 1 -1 -1 1
w2 =-1 -1 1 1 -1 -1 1 1 -1 -1 1 1 -1 -1 1 1
Im about to multiply m2 with w2
Should i multiply m2 with all of w2
(1 * -1 -1 1 1 -1 -1 1 1 -1 -1 1 1 ...
1
vote
4answers
169 views
A better explaination for 'there's no flipping of the impulse response' [closed]
I showed the question about flipping the impulse response to some math teachers and electrical engineers at an university. They read Dilip's answer and thought that it was hard to understand what ...
1
vote
3answers
75 views
Image processing, recognizing a small feature in a larger image
I am trying to write an image processing program to recognize bubbles in oil.
It has been suggested I try computing the convolution of the image and an image of a typical bubble.
i.e. : ...
1
vote
2answers
52 views
When should the sum of all elements of a gaussian kernel be zero?
I found an approximation of a 5x5 2D convolution kernel like this :
Here, the sum of the elements is zero and this one was used for Laplacian of Gaussian!
Another one here :
This one has all ...
2
votes
1answer
57 views
How to show that this filter is a HP filter
i got a system with transfer function given by:
$$H(\omega)=1-e^{-j\omega}$$
I already plot it, and that seems to be a periodic function with $H(0)=0$, $H(\pi)=2$, , is that enough to show that this ...
1
vote
1answer
42 views
Where does convolution fit in DFT?
I am trying to understand where does the convolution fit in Discrete Fourier Transform. I know that convolution is producing a third signal from two other signals. I also know that DFT transforms one ...
0
votes
0answers
15 views
Consider filtering n*n images by separable m*m filters.What are the computation time for filtering using FFT;2-D convolution;by two 1-D convolutions
Consider filtering square n*n images by square, separable m*m filters.
a) Give general equations for the computation time for the following approaches to this 1) filtering using FFT 2) by 2-D ...
-1
votes
3answers
108 views
Understanding convolution
Take:
$$
(u*v)(k) = \sum_{i=-\infty}^\infty u(i)v(k-i).
$$
The $k$ is there, it's because you want to define
$$
\ldots\ldots, (u*v)(-3), (u*v)(-2), (u*v)(-1), (u*v)(0), (u*v)(1), (u*v)(2), ...
0
votes
1answer
65 views
Computation time 1) fft, 2) 2-d convolution, 3) two 1-d convolution
Consider filtering square n*n images by square,separable m*m filters. What are the general computation time for the following approaches 1) FFT 2) by 2-D convolution 3) by two 1-D convolutions. ...
1
vote
0answers
40 views
Reconstruction from Convolution
I am trying to implement Wavelet transform in an embedded environment. The problem I face goes like this:
Two vectors, A and B. A is input samples. B is vector co-efficients.
I take convolution of A ...
1
vote
1answer
35 views
How to apply convolution on a buffer
I'm trying to do some simple filtering for an audio signal using a window-sinc low pass filter. Supposing that my buffer has M values and the filter kernel size is N, after convolving these two arrays ...
4
votes
2answers
159 views
Simulating analog filter using convolution or converting with fft
My task is simple; I want to simulate analog low-pass filtering of an input signal, using Python. Note that the input signal is an array of values, not an analytical function.
My first question is if ...
2
votes
1answer
97 views
Deconvolution in Python
I'm trying to use and understand SciPy's deconvolve for a project I'm working on. I'm having some trouble understanding how to use it.
What I would like to do is to take two PMFs from discrete ...
3
votes
0answers
63 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 ...
3
votes
1answer
83 views
How do I find the Hilbert transform (qudrature) of a discrete signal by convolution with a Hilbert kernel?
Given a discrete real signal $ f_{re}(t) $ the (complex) analytic signal is given by:
$ x(t) = f_{re}(t) + j*f_{im}(t) $.
I want to calculate $f_{im}(t)$: the quadrature by convolving with a Hilbert ...
1
vote
1answer
51 views
How can I calculate the cyclic (periodic) convolution?
I'd like to understand how to calculate the cyclic convolution as well as understand what that means exactly. How should I go about finding the output for various periods for a system?
I have an ...
3
votes
2answers
82 views
How to find the input if I have the impulse response and the output of a finite sequence?
I understand how to find the output from the input with an impulse response, but how can I go about finding the input if given the other two?
I have $y[n] = [-1, -1, 11, -3, 30, 28, 48]$ and $h[n] = ...
0
votes
0answers
34 views
Implement average as correlation
I have a MxN image matrix in, and need to get out matrix out size MxN as follows:
Each point out[i,j] is the average of all in[i,j] inside a window size WxW (if boundary allows). For example if W=10
...
2
votes
1answer
98 views
Given f(x) and its FFT F(u), I need to prove that df/dx = F(u)*2iu(pi)/n
Given $f(x)$ and its FFT $F(u)$, I need to prove that $df/dx = F(u) * 2iu\pi /n.$
$df/dx = f'(x)$ and $n$ is the number of pixels of the one dimensional image $f$.
I tried to use the convolution ...
0
votes
0answers
41 views
how to pad the zeros
i have to do the convolution of two signals by employing FFT. as i am new to programming, please tell the steps that how to pad the zeros to signals to make it of equal length as the number of fft ...
3
votes
1answer
179 views
Get an input signal from LTI system output, find impulse response
I just study signal processing and I have some questions.
How to find impulse response $h[n]$ sequence of the system if I have
$x[n]$ and $y[n]$ (input and output) sequences? Hope there is a formula
...
4
votes
1answer
124 views
Common use cases for 2D NONseparable convolution filters?
In the image processing world, I've noticed that a lot of the popular convolution filters are separable. Here's a quick list of common separable filters:
Sobel
Gaussian blur
Box filter (all ones, ...
0
votes
1answer
146 views
1
vote
1answer
105 views
Convolution in image processing ?
I got the concept of Convolution in signal processing from a video lecture that it is method to get the area overlapped between two signals when one signal is flipped over and traversed over another ...
3
votes
1answer
73 views
Help Understanding Convolution Filter Formulation
I'm reading Computer Vision: Algorithms and Applications wich is available online as a PDF and on Chapter 3.2 page 111 it introduces convolution operators for images giving the formulation:
$g(i, j) ...
7
votes
0answers
195 views
How to deduce a linear system's impulse response from a set of input/output signals?
I want to know how to solve those types of problems.. is it by inspection ?
Consider the linear system below. When the inputs to the system $x_1[n]$, $x_2[n]$ and $x_3[n]$, the responses of the ...
1
vote
1answer
73 views
How to properly perform convolution on bitmap image?
Correct me if I'm wrong, I should read bitmap into matrix of float values where I would get numbers up to little more than 16*10^6, then I should expand my image matrix to size 2^k putting the ...
5
votes
2answers
336 views
Circular and Linear Convolution
What is the difference between circular and linear convolution? When would I choose one over the other? In image processing where a filter is applied to an image with a mask which type of convolution ...
2
votes
2answers
84 views
Breaking a convolution into smaller pieces
For a project I need to do convolution and i use gpu for calculations. Sometimes I have to deal with kernel sizes of 50x50 and this size of kernel is sufficiently large that it chokes the gpu. (not ...
0
votes
0answers
24 views
Covolution of DTFT [duplicate]
Possible Duplicate:
Convolution and DTFT
$x_1(n)=x_2(n)=1$
where $0 ≤ n ≤ N-1$
1)The linear convolution of the signal gives a triangle how you write it in mathematical form?
The DTFT of ...
7
votes
4answers
480 views
Flipping the impulse response in convolution
During convolution on a signal, why do we need to flip the impulse response during the process?
1
vote
0answers
88 views
Applying a filter kernel defined by a continuous equation in the frequency domain
I have a filter kernel $K(\omega)$ completely defined in the frequency domain as a continuous function of angular frequency $\omega$. I know $K(\omega)$ defined as a continuous mathematical equation.
...
3
votes
1answer
78 views
Where to get the Kodak PhotoCD raw image dataset?
I've been doing some background reading on demosaicing raw images.
I've seen the Kodak PhotoCD raw image dataset mentioned in a few papers on demosaicing:
Image Demosaicing: A Systematic Survey
High ...
1
vote
2answers
161 views
Decoding Matrix Encoded Surround Sound Through Convolution
I wish to create a finite impulse response filter to decode a dolby digital matrix encoded 2 channel signal into 5 channels. These filters would then be used in a realtime pipeline on a Linux machine ...
4
votes
3answers
1k views
What is the physical meaning of convolution of two signals?
If we convolve 2 signals we get the third signal, what do this third signal will represent in relation to the input signals?
1
vote
1answer
73 views
Understanding the frequency scale of a spectrogram
The graph below was derived from a raw seismogram recorded during an earthquake over a timespan from t=0 to t=1400 seconds (not shown on x-axis).
The original seismogram $s(t)$ is not shown, but it ...
1
vote
1answer
46 views
Verifying the computation of a convolution
I have an input signal $$x(n)=\left(3,-5,4,3,-1,-2,6,8\right), n=-3,..,4$$ and impulse response $$h(n)=(1,-1,1,-1,1), n=-1,...,3.$$
The convolution between $x(n)$ and $h(n)$ is
...
2
votes
2answers
115 views
Linear predictive model convolution
Accidentally asked this question in the general area and was told to ask here, so...
I've been trying to develop a lightweight, relatively-fast-to-decode sound compression format for use in my gaming ...
4
votes
1answer
139 views
Why idft(dft(a) * dft(b)) not equal to convolve(a, b)?
I'm a little confused... I always thought the DFT of a convolution was equal to a product of DFTs, but when I tried this in Python:
...
7
votes
1answer
132 views
Convolution involving turning each pixel value to the most represented pixel value of the neighbourhood
In order to correct gradual changes of intensities in the background of grey-scales images, I have been blurring them and then subtracting the original images from the convolved one.
In some cases, I ...
4
votes
0answers
183 views
How do I implement the 3D structure tensor in C/C++?
I am trying to figure out the details on how to implement the 3D structure tensor in C/C++ in an easy but efficient way and need some advice!
For a discrete function $ I(x_i,y_j,z_k)$ the 3D ...
3
votes
1answer
273 views
Convolving two signals
I saw a video where this guy used a program to do a frequency analysis on a voice signal and a sawtooth wave (I'm assuming this was FFT). Then he saved the plots as images and combined them pixel by ...
2
votes
0answers
131 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:
$s_{\rm out}[n] = s[n] \ast k[n,q]$
...
7
votes
5answers
642 views
Why do linear systems show sinusoidal fidelity?
I am looking for a proof for sinusoidal fidelity. In DSP we study a lot about linear systems. Linear systems are homogenous and additive. One more condition it satisifies is that if a signal is a sine ...
2
votes
2answers
242 views
What type of circuit is responsible for convolution in the classic analog telephone?
I'm interested in learning how telephones work, so I did a little bit of reading about signal processing. When I came up with the word convolution, I quickly realized the importance of this term.
To ...
2
votes
1answer
2k views
Difference between linear convolution and circular convolution for a kernel
If I understood correctly (and this page should confirm: http://www.cs.ioc.ee/~khoros2/linear/convolution-teo/front-page.html)
if I convolve linearly (the usual point-to-point multiplication and ...
2
votes
1answer
98 views
Kernel convolution in frequency - weird “padding”
I don't know whether this is the right place to post this, but I suppose it is.
I know that frequency multiplication = circular convolution in time space for discrete signals (vectors).
I also know ...
16
votes
2answers
3k views
What is the difference between convolution and cross-correlation?
I've found on multiple sites that convolution and cross-correlation are similar (including the tag wiki for convolution), but I didn't find anywhere how they differ.
What is the difference between ...
10
votes
1answer
899 views
Overlap-Add versus Overlap-Save
What differences or other criteria can be used to help decide between using overlap-add and overlap-save for filtering? Both overlap-add and overlap-save are described as algorithms for doing FFT ...
3
votes
1answer
423 views
Transpose of convolution
I have an $n \times n$ asymmetric convolution kernel, $k(t_1,t_2)$. $k$ is zero everywhere except for in small regions near the corners.
I also have an $n \times n$ image, $f$.
Let $*$ denote ...
