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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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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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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23 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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33 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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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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43 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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2answers
150 views

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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64 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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62 views

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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46 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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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
82 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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1answer
64 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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48 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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91 views

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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107 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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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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1answer
174 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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110 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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45 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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33 views

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
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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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174 views

why is multiplication faster than convolution?

I have the following matlab code ...
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1answer
116 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
90 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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1answer
56 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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56 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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139 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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69 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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273 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 ...
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Difference between correlation and convolution on an image?

Could you please clearly explain what is the difference between correlation and convolution that is down by a filter on an image? I mean in terms of signal processing definition I know that ...
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Convolution that results in an all-zero sequence

I am asked to find a pair of sequences, each one of which contains three distinct values and where the convolution is an all-zero sequence. I've came to the conclusion that one of the sequences must ...
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1answer
2k views

Apply a Gabor filter to an input image

I tried to apply a Gabor filter with a specific scale (according to my values of lambda and sigma, so it is 7x7) and for 4 orientations (0, pi/4, pi/2 and 3pi/4) to a input gray scale image. In my ...
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Find output of digital filter given input and transfer function?

Hey guys so I have an input sequence that are real values that represent intensity of a column of an image. I also have the transfer function in the Z domain of a 2nd order high pass filter. I have ...
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38 views

Using Fast Convolution to apply HRIR to soundwave

I have a dozen source sound waves; each is about one second duration. I want to put each one through a digital filter (I'm truncating it to 128 taps). Currently I'm doing this with a bog standard ...
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101 views

Can two nonzero signals $x[n]$ and $y[n]$ give a zero convolution

Suppose $x[n]$ and $y[n]$ are two nonzero signals(i.e., $x[n] \neq 0$ for at least one value of n and similarly for $y[n]$).Can the convolution between $x[n]$ and $y[n]$ result in an identically zero ...
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Conceptually, how does real time convolution reverb work?

I've got an impulse response of a hall, it's 10 seconds long. Now say I want to apply this reverb to a wav file of some singing. I would perform a convolution of the data in two wav files and that ...
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80 views

Determining linearity, causality, memory, and time invariability from a picture of the signal

So, this is a picture of saccadic eye movement reflected by an EOG. How can I determine if the eye movement system is linear, causal, memoryless, and time invariant from this displayed waveform? ...
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60 views

Is it meaningful to find linear convolution of just two random sequences? [closed]

Could it bring any meaning? Is this kind of convolution be useful is solving anything?
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81 views

Basic Convolution Reverb Question

I'm surveying for feasibility techniques for a potential future project that's rather out of my past areas of expertise, and I have a fairly basic question. Of course if it looks feasible I will have ...
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109 views

Mathematical proof of relationship between derivative and convolution

What I'm looking for is the mathematical proof of why we can calculate derivatives as a simple convolution of a mask, and how do we get that mask? I know it has something to do with how the derivative ...
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288 views

Savitzky-Golay Filter Coefficients and Wikipedia

I am trying to implement a Savitzky-Golay filter by following this Wikipedia page and in the first instance I have written the following Octave software code to create the convolution coefficients ...
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2answers
85 views

Simplification of a convolution-like expression

I am trying to further reduce the following expression (if there's a nicer way to write it): $\sum_{k=-\infty}^{+\infty}\sum_{p=-\infty}^{+\infty} \sum_{l=-\infty}^{+\infty} w(k) ...
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Need help understanding convolution indexing

Ok, this is leaving me increasingly frustrated. This builds on a previous question here but I am still not getting the indexing, although I learned from that question all the same. Case 1: First ...
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What are the problems with designing an FIR filter using FFT?

I'm trying to get an understanding of the relationship between an FIR filter designed from "first principles" using a filter kernel with convolution, and a filter designed in one of two ways using FFT ...
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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 ...