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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Convolution: 2D kernel to full matrix

We know that a convolution can be replaced by a multiplication with a toeplitz circulant matrix. Meaning, assume I have convolution kernel $h$ and matrix $I$ (of size $m \times m$ for example), then ...
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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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Confusion about result of FIR All-pass filter design

I try to design a FIR All-pass filter with random phase in the frequency domain. I am a bit confused by my result and am not sure if the reason is a programming error or a misconception about ...
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1answer
40 views

Discrete Fourier Transform and Opposite Convolution Theorem

I am reading the Wiki for DFT. There is a part for circular convolution theorem which sounds a bit odd saying: $$ \mathcal{F} \left \{ \mathbf{x\cdot y} \right \}_k \ \stackrel{\mathrm{def}}{=} ...
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2answers
43 views

Convolution theorem

As stated by the convolution theorem, a convolution in spatial domain is equivalent to a multiplication in the frequency domain.Nevertheless, when should the first be preferred over the latter?
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How to calculate step and impulse response at multiple sampling rates

I'm struggling with a basic concept. Suppose I have a system $y(t)=e^{-at}u(t)\ast x(t)$ and I want to plot impulse response and step response using Matlab conv() function at various sampling rates. ...
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41 views

Why does the odd multiple of $\frac{\pi}{4}$ on Gaussian cause loss in repeatability under image rotations?

I couldn't figure out below paragraph on SURF paper and hope that someone can help me to understand it. Why image rotations around odd multiples of $\frac{\pi}{4}$ lead to a loss of repeatability? ...
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403 views

Deconvolution by convolution

This is now a second time I am attempting to ask this very important but simple question here. What I want to know is can you do deconvolution by convolving a signal. It is often stated that, for ...
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25 views

Impact of different padding schemes in Frequency domain image filtering

I understand, that image padding is necessary in order to prevent wrap-around effects due to circular convolution. My set of questions are related to different padding schemes. Zero Padding is easy ...
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59 views

Finding linear convolution of two time series

PROBLEM Two real, causal time series $$f_k = a^k \quad \text{and} \quad g_k = b^k$$ where $a \neq b$, $|a| < 1$, and $|b| < 1$, are given for $k = 0,1,2,...$ Find the linear convolution ...
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41 views

Why the delta at the end of the approximation?

The equation to approximate an input signal with a unit impulse in Continuous Time, is shown below, before we take the limit ...
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27 views

Fast convolution with striding step

I want to convolve two discrete functions $f$ and $g$ using convolution stride size $a$ to get the result as $s_{a, i}$: $$s_{i,a} = \sum_i g_k f_{ai-k}$$ I know that simple convolution with $a=1$ ...
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25 views

Normalisation of delay-addition comb filter implementation

I'm trying to write a tempo detection algorithm for analysis of audio samples. I'm roughly following the approach described in Scheirer, the first stages of which give me some very nice beat onset ...
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1answer
40 views

Convolution from bottom right [closed]

I want to do a convolution from the bottom right and not as usual from the top left. I think conv2 of Matlab only does from the top left. How can I do a convolution in Matlab from the bottom right? ...
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68 views

circular Convolution

Multiplications of time domain vectors of two signals is equivalent to convolutions in frequency domain and also use circular convolutions for when FIR filter design using window method in frequency. ...
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50 views

Convolution sum vs auto-correlation problem

I had an exam one of these days and one of the questions was: "Knowing that an auto-correlation estimator of a sinal x[n] could be defined by: $$ R_{xx}[k] = \sum_{n=-\infty}^{+\infty}h[n].x[n+k] , ...
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35 views

DFT method for a sequence defined by recursion

I encountered the following interesting computational problem in the field of computational statistical mechanics. https://www.dropbox.com/s/8yimd9uy5u0jrdj/dftpr.pdf thank you :)
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1answer
87 views

Continuous-time mathematical formula for deconvolution filters

I have an elementary function $p:\mathbb{R}^2\rightarrow\mathbb{R}$ which (locally) represents an image. It's a polynomial, and its the result of the following 2D convolution: $$p=f\star G\star ...
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36 views

How to create a convolution matrix with a variable condition number(CN)

I want to know the performance of a deconvolution algorithm with different CN, so I'm convolving my signal with different convolution matrices(different CNs) and then applying the deconvolution ...
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Operaion on Simple Discrete Time Signal , Very Simple Question

I got this simple Discrete time signal question on which i have to perform shifting and multiplication.But I have some Doubt regarding the answer this book shows. Please see the uploaded image.
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63 views

Convolve a minimum phase wavelet with delta peak

let's assume I have two time series: one with a delta peak at position $x$ and another time series with a minimum phase wavelet that starts at time $y$ with a maximum peak at position $z$. Now, when ...
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3answers
74 views

Connection between filter equation in frequency domain and difference equation in time domain?

I know that the frequency response of a filter is described by equation: H(w) = 1-1.176*e^(-jw) + e^(-j2w) , where w is the angular frequency. Then in time domain ...
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1answer
53 views

How to calculate the zero state response?

In the following question and answer I kind of get it how it is calculated at surface but I don't get it fully. Can someone please explain the answer in depth?
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Convolution in the frequency domain

We often hear that "convolution in time is the same as multiplication in frequency", and vice versa, that "convolution in frequency is the same as multiplication in time". So in a typical windowing ...
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1answer
68 views

Is it possible to open up this particular convolution equation?

I have three vectors, $x[n]$, $w[n]$, and $z[n]$. I need to compute: $y[n] = z[n] * \Big(x[n] \cdot w[n] \Big)$. This is easy to do. However, is there a way I can do this by 'opening' up the ...
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convolution of signal with wavelet

I know that the complex wavelet transform is given by $$\int_{-\infty}^{\infty}f(x)\psi^*_{s,u}(x)\,dx$$ where $f$ is the signal, $\psi_{s,u}(x)=\frac{1}{\sqrt{s}}\psi(\frac{x-u}{s})$ is the wavelet. ...
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group delay of an fir filter

suppose we have an fir filter: t=[-50:50]; x=[sinc(.1*t).*cos(2*pi*.15*t),sinc(.1*t),sinc(.1*t).*cos(2*pi*.3*t)]; using matlab command grpdelay(x,1),we observe the groupd dalay of the system. then we ...
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59 views

convolution and frequncy response

I have a sinusiodal signal x in time domain.I have done the convlotion as followings using matlab: y=conv(x,x) and ...
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48 views

How do I combine a copy of a signal with the original to achieve a chorus effect in a .wav file using Python?

Can you please explain or point the right way to think about how to implement two sound effects in a .wav file. So I read a .wav file and converted it to int values (in ...
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7 views

Encoding signals to selectively mute out when recording

Pardon my bad description but I am not from elec background. I have say 3 sources S1, S2 and S3 at positions X1, X2 and X3. I have 5 receivers R1 through R5 at positions Y1 through Y5. Can you ...
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1answer
87 views

How do you deconvolve irregularly sampled points?

$f:\mathbb{R}^2\rightarrow\mathbb{R}$ is an unknown signal, and $g:\mathbb{R}^2\rightarrow\mathbb{R}$ is a known point-spread function (in my particular case it's just a Gaussian). A system samples ...
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71 views

Easy Filter with FFT and Convolution

I'am pretty new to this topic so i dont have much experience with DSP. I want to filter(highpass) a WAVE file, i have already programmed the FFT, and now want to filter the FFT vector via convolution ...
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73 views

Convolution theorem with a kernel smaller than the image

Suppose that I need to apply a convolution filter to an image. I want to do it by using the convolution theorem so I compute the kernel for the size of the input image to later calculate fft's and ...
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Can I construct a linear system so that it results in a moving average?

I've just learned about linear systems and impulse response functions. I know that in a linear system consisting of $h_1[k]$ and $h_2[k]$, the impulse response of the system is $h_1[k] \ast h_2[k]$. ...
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156 views

Applications of Correlation in Signal Processing

There have been discussions on the differences between convolution and correlation, autocorrelation, cross-correlation, et al. In spite of looking at the visualizations, and understanding the ...
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95 views

Convolution of an image with a kernel that is a product of two functions

Suppose that $G(i,j)$ is a Gaussian decay function on the distance between points $i$ and $j$ of an image. In addition, $D(i,j)$ is the difference between the VALUES of the image at those points. ...
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339 views

conv2 is faster than imfilter

A lot of people use imfilter to achieve a 2-D convolution between an image and a filter, but the majority of people use conv2 ...
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137 views

Equivalence of convolution through polynomial and matrix products

I am trying to understand the equivalence of convolution through polynomial (coefficient) multiplication, Fast Fourier Transforms, and matrix multiplication. I am using octave with the octave-signal ...
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1answer
50 views

Interpreting FFT coefficients from system matrix that is originally Toeplitz (but not circulant)

If I have a measured signal $y$, true signal $x$, and a convolution matrix $A$ that is a Toeplitz but not circulant matrix, I can write the convolution as \begin{equation} y = A x \ . \end{equation} ...
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Convolution in Continious time

Dear all, Please find attached image, I am not able to understand why is the underlined term is to be included. Shouldn't it be simply the exponential term?
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1answer
110 views

Convolution kernels for image filtering

As I understand it, in image processing, when it is desired to apply a filter of some sort to an 2D image, a kernel is applied to all the pixels of the 2D image in a process called convolution. ...
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190 views

why is multiplication faster than convolution?

I have the following matlab code ...
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1answer
191 views

SVD is not applicable to time series analysis?

I am studying a deconvolution problem for which observations include noise. I am considering using one of several common regularization methods, including Tikhonov's solution, truncated Singular Value ...
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1answer
111 views

Filtering an image with two gabor filters

I have an image of size 160x160 of pixels. I am trying to convolve this image with two Gabor filters of different scales (7 and 9 respectively) but with the same orientation. I red in an article the ...
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66 views

Convolution in image processing

Does anyone know how to write arg min code in matlab with explanation? I am referring to a paper for my research. I am not sure whether I can paste the paper link here. At first, I try to do feature ...
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1answer
58 views

What kind of discrete convolution is this?

Let x[n] and y[n] be defined for n=0,1, ..., N-1. This (for example with Python's scipy fft ...
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193 views

Convolution for non-signal-processing background

I am a civil engineer and am analyzing traffic data recorded by capturing vehicle movements over a highway for a specified time period. The database I am dealing with contains observations at every ...
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72 views

Fourier Transform & Convolution to get response - confused

in the past couple of years I've always been using Laplace transform for system responses, but today tried to do it with Fourier transform and failed. What am I doing wrong? If we have a signal $x(t) ...
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422 views

What is spatial correlation and spatial convolution?

What does the term spatial correlation and spatial convolution mean with respect to digital image processing ?
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Convolving time reversed discrete input with time reversed discrete impulse response

Question 3.1 d from Chapter 3 of Oppenheim's Signals & Systems I have $$x[n]=(-1)^n{u[-n]-u[-n-8]}$$ $$h[n]=u[n]-u[n-8]$$ and the question asks for $y[n]$ which is the convolution of $x[n]$ and ...