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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Confused with convolutions in scipy

I tried to write my own circular convolution function in python using the fact that for two signals $f$ and $g$ we have $$ \widehat{(f * g)} = f \cdot g $$ So I tried this ...
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27 views

What is a mask? [closed]

I have seen one sample mask -1 0 1 -1 0 1 1 0 1 Could you explain how mask is a filter and what are the differences between them? How can i increase the mask ...
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27 views

Fast/efficient way to compute Laplacian edge enhancement filter

I would like to implement a somewhat smarter Laplacian edge enhancement convolution. Right now it is implemented as (generic 3x3 convolution): ...
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1answer
28 views

Filtering Passband Signals using Complex Baseband Filtering

So I'm given a pass band filter with specific transfer function $H_p(f)$, I want to implement this via baseband processing. I already know how to take the input signal $u(t)$ and process it such that ...
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1answer
34 views

Is there a convolution mistake in my method?

I have the input signal $x(t)$ And impulse response $h(t)=20 e^{-1000t} u(t)$ in which u(t) is the unit step function. When I try a convolution, I thought the solutions would be something like: $ ...
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1answer
17 views

Problems filtering image with prewitt

I'm trying to filter an image vertically to get the edges, in MATLAB, but I get very different results from convultion and correlation. CODE: ...
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44 views

convolution of a real and complex signal

How do we define convolution of: $$x(t)= \mathrm{sinc}(W t)$$ and $$y(t)= -j\mathrm{sinc}(2W t)$$ Answer: In the frequency domain, both of them are rectangular functions and multiplication of them ...
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2answers
170 views

Understanding circular convolution

Let $a$ and $b$ $\in \mathbb C^N$ and $a[k] = a[k \mod N]$ (same with b). Then the circular convolution of $a$ and $b$ is defined by $$ (a * b)[n] = \sum_{p=0}^{N-1} a[p] b[n-p].$$ I have a problem ...
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44 views

applying convolution theorem swaps quadrants

For educational purposes I implemented the DFT and inverse DFT for images using OpenCV. Applying the DFT to an image and taking the inverse DFT of the spectrum yields the original image, so this ...
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33 views

Are convolution and deconvolution kernel the same?

I need to clarify this and rather confused by this. Lets say: $x = h * g$ $x$ - measured data $h$ - raw data $g$ - instrument response function (convolution kernel) So lets say I ...
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18 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 ...
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2answers
55 views

convolution matrix for image scaling

Is there any way how to compute convolution matrix for Nearest Neighbor (bicubic, bilinear) image scaling (upscale/downscale)?
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60 views

Implementing overlap add method for convolution with a slice of the filter

In overlap add method for convolution a filter $x$ of length $M$ will get convolved with a signal $y$ of length $N$ where $M << N$, i.e., $z = x * y $. Here the signal $y$ is sliced into ...
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18 views

Equivalence of transfer functions based on identical input and output

We have two transfer functions which are functions of frequency. No matter the frequency value of the input, which is of the form $e^{jwn}$ or the value of n, the output will be identical. Are the two ...
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24 views

Convolution / Correlation correct implementation in java

I have a java programm which is manipulating an RGB picture which comes in a 3dimensional matrix. I tried to implement an apply Convolution and an apply Correlation function, which applies a kernel ...
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0answers
22 views

N-point circular convolution with n > length of sequence

If I want to take an n-point circular convolution and both of my sequences are less than n length, how do I do this? Do I cutoff the terms that don't fit? For example, say I want to perform 4-point ...
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1answer
49 views

Prove that time-reverse yields inverse filter for deconvolution?

In reading literature on the construction of impulse responses from sine sweeps (e.g. papers by Farina), I see it stated over & over that the way the impulse response is constructed from a ...
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1answer
78 views

How to show that y[n] = x[n] * h[n] turns into the Y(z) = X(z).H(z)?

I'm trying to show that $y[n]=x[n]*h[n]$ turns into $Y(z) = X(z)H(z)$ in Z-domain by first applying convolution then by taking the inverse Z-transform of the $Y(z)$, stating that it's the same ...
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1answer
47 views

Efficient algorithm for computing area under convolution?

Consider $N$ discrete signals $x_1(n), x_2(n), \ldots,x_N(n)$ each a bounded support of size $M$. To convolve them, we can zero-pad each of them, multiply their FFTs, and take the result's inverse ...
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34 views

How can you intutively figure what the impulse response will behave like?

I was trying to understand convolution from this book and came across this figure: Here, the input signal is a combination of a sine wave and a ramp. In fig a, the input signal is convolved with a ...
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32 views

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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22 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
84 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
67 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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4answers
295 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
55 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
22 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
40 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
90 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
73 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
79 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
106 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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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
77 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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47 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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103 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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107 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
71 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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61 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
378 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
49 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? ...
3
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2answers
469 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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43 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
76 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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36 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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35 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
113 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
102 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] , ...