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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Size obtained by applying Linear convolution

We know that applying a filter on an image is called correlation or convolution depending on the filter angle. In Gonzalez I have read that we can apply linear convolution on an image. Here I have a ...
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1answer
30 views

Matlab: Convolution of two Spectra [on hold]

I have two spectra one is a LED Spectrum which i plotted plot(intensity, wavelength) and another Raman Spectra, which was plotted by two 2 variables. ...
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19 views

What is the difference between Time-Frequency Represenation and TF Decomposition

I'm asking as I'm looking at Wavelet transforms, and I see that it is possible to have a TF decomposition or a representation of the signal. Looking for example at the code here we can see that the ...
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1answer
54 views

2D deconvolution of recorded electron beam data

I'm currently working on a project that involves using an electron gun and it would be really nice to know the spot shape of the electrons coming out of the gun (the frequency of electrons at some x,y ...
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1answer
34 views

Difference between correlation/convolution and matrix multiplication

Can anyone please clarify the difference between correlation/convolution and matrix multiplication? As I thought either convolution or correlation is similar to matrix multiplication. I read this ...
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37 views

Prove the convolution of 2 causal systems is linear and time invariant

I'm wondering how to prove this. I know what the convolution integral looks like: given $f(t)$ and $g(t)$ it's: $$\int_{-\infty}^{\infty}g(t-\tau)f(\tau)d\tau $$ How does the term causal relate ...
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4answers
90 views

What is convolution of two sine waves (tones)?

Convolution of two sine waves (or tones as called in audio) is theoretically not defined as the integral is infinite. Taking finite duration windowed sine waves and doing there convolution ...
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1answer
50 views

Avoiding edge repeats in a FFT convolution

I am trying to use FFT as a fast way to convolve a image, however one of the downsides of this is that the "kernel" image will repeat when reaching the edges of the sample. Is there a way to avoid ...
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1answer
15 views

Different results for seperable filtering v/s direct filtering on 2-D image in MATLAB

I compared the difference between seperable and direct filtering for MATLAB's cameraman image. The difference is huge. I would like to understand the reason for this. Code below. ...
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1answer
35 views

Convolution of h(n) & x(n)

can anyone please help me with finding Convolution for following problem ..... 1) $h(n) = \delta[\sin(1 + |n|)]\quad \text{and}\quad x(n) = \sin(n^2)$ 2) $h(n) = \delta[\sin(2\pi n/N)] \quad ...
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2answers
41 views

Convolving Room Impulse Response with a Wav File (python)

I have written the following code which is supposed to put echo over an available sound file. Unfortunately the output is a very noisy result which I don't exactly understand. Can anybody help me with ...
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1answer
68 views

How to derive the answer to this convolution problem?

I came across this below question, (which was a homework assignment question for Signal Processing class, which my friend mailed me for help solving), mulled over it for an hour and had no idea how to ...
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1answer
53 views

understanding discrete-time convolution in LTI systems

I'm trying to understand the discrete-time convolution for LTIs and its graphical representation. standard explanations (like: this one) start with the idea of decomposing an input signal $x[t]$ into ...
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2answers
87 views

Difference between convolution and multiplication of freq. response and freq. spectrum

Suppose I have impulse response like [1/25,2/25,3/25,4/25,5/25,4/25,3/25,2/25,1/25]. I did convolution with 600 samples of test signal (it seems that I did some filtering). Then I calculated the ...
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0answers
14 views

Extraction of a decision boundary (LDA) after a systematic querying of the feature space and convolution with Sobel filter (examples in numpy)

I am doing some experiments with LDA (Linear Discriminant Analysis), in python. Now I am at the point in which I would like to display the separation planes in the 3-dimensional feature space. I ...
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1answer
74 views

Writing a Discrete Fourier Transform program

I would like to write a DFT program using FFT. This is actually used for very large matrix-vector multiplication (10^8 * 10^8), which is simplified to a vector-to-vector convolution, and further ...
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30 views

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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88 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?
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1answer
77 views

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
56 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
56 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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2answers
170 views

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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1answer
45 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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2answers
442 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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0answers
33 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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1answer
68 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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2answers
43 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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30 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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27 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
42 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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1answer
90 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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1answer
79 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
110 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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2answers
52 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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26 views

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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1answer
68 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
76 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
80 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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358 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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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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2answers
235 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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101 views

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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1answer
73 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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0answers
53 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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8 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
88 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
77 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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2answers
90 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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2answers
99 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 $h_1[k] \ast h_2[k]$. ...