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Questions tagged [convolution]

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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FIR filter usage / understanding FIR

Let us assume that I wouldd like to create a digital lowpass with 5 taps. I am not using a window function but just the impulse response from my Fourier integral. I get the following coefficients: $h=...
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1answer
135 views

LTI filtering for wide-sense stationary process

Why is it that if $U[n]$ is wide-sense stationary and it is convolved with $h[n]$ to produce $W[n]$, the autocorrelation becomes $R_{WW}[n] = R_{UU}[n]*h[n]*h[-n]$? I know that in general $R_{WW}[n_{...
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4answers
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A music recommender system by using basis functions

So my university project is about music recommender system. My teacher not saying too much. But he only said it will use basis functions and convolution technique. That's all i got from him. I want ...
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403 views

Examples for two functions/signals that have same autoconvolution and two signals that have same autocorrelation

I would like to know two functions that have same autoconvolution(convolution of a signal with itself) and two other functions(not necessarily above two) that have same autocorrelation
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1answer
67 views

How do I efficiently evaluate a convolution integral between different-sized domains?

This is a question that I've previously asked over on math.stackexchange, and I have yet to receive a useful answer. It was suggested that I post this here. The problem itself originally comes from ...
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0answers
129 views

Appropriate digital filter for GPS tracks?

I have an open-source software project whose purpose is to analyze a GPS track, or a similar track made by an application such as google maps, and estimate the physical exertion required to hike or ...
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2answers
234 views

Can I compute convolution through the overlap and add method without the IFFT?

So, I'm (I think) aware of how the overlap and add algorithm for linear convolution works, but my question is that, suppose I have a FFT-ed set of sequences that belong to a large sequence. Can I add ...
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2answers
260 views

the sub-range of circular and linear convolution

circular convolution $x_{_3p}[n]$ = $x_1[n]~\circledast_N ~x_2[n]$ is a period version of the linear convolution $x_{_3p}[n]=x_1[n] * x_2[n]$ The length of $x_1[n]$ and $x_2[n]$ are $L$ ($n\in[0,\...
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0answers
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Locate first minima in signal

I have many datasets which all looks roughly like this: All the datasets have this in common. First there is an artifact around 0 with an unknown (but likely very high) intensity. Then there is some ...
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1answer
131 views

convolve to differentiate black and white colors

a figure for instance of size 500*500 has half above part with black and below half white should result in a white line where the white meets the black (something like a single line at line 250 with ...
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1answer
343 views

Can someone explain what a butterfly is in regards to DSP?

I often see the term "butterfly" in discussion and methods relating to DSP. What is a "Butterfly?"
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2answers
123 views

Understanding DFT-ODD operation in Gardner Efficient Convolution paper

As a newbie to DSP I am trying to understand and implement an efficient convolution engine as per JAES V43.3 1995/03 - Gardner - Efficient Convolution without I/O Delay. I'm pretty much there with a ...
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905 views

DFT - Removing window effect in spectral domain with convolution

I was thinking about the DFT windowing subject and a thought came to my mind. A DFT will yield the spectrum of a signal convoluted with spectrum of the window used, therefore having a main lobes and ...
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3answers
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Deriving the Convolution Kernel of the Inverse of a Signal

Let $y$ be the inverse (in the sense of convolution) of $x$, i.e. $$x \star y = \delta$$ Context: $x[n]$ is a discrete signal defined for $n = 0,\ldots, N$. We can assume $x[n] = 0$ if $n \not\in [...
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3answers
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Sweep signal + microphone-recorded signal => Impulse response

I played this signal A (a 20Hz to 20000Hz sinusoidal sweep in 10 seconds) with a studio monitor speaker in a big church, and I recorded the result B with good microphones. The result is very reverb-...
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1answer
463 views

Is there any difference between using convolution and correlation for finding edges with Sobel?

I know that Sobel is a filter for edge detection and we should use convolution to find edges, but is there any difference if we use correlation instead of convolution? I think Sobel tries to find a ...
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1answer
86 views

suitable application for 2d FFT

I have been building a convolution library for multichannel audio and am using FFTW as the main FFT transform library. There are 4 channels of audio in play at any one time and they are interleaved, ...
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1answer
354 views

DFT and IDFT deriviation problems

[![enter image description here][1]][1] For this problem: Actually,i think that the question asks us to get the IDFT from the DFT,so I did it..but I am not sure,till now, whether this problems asks ...
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1answer
53 views

How to calculate the output image with the following kernel?

What is the advantage of using this equation? I guess we may use Taylor series, but I tried my best and could not get the equation.
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55 views

deconvolution challenge

OK hive mind... i have two identical fixed-size signal buffers, each containing 4 channels of audio. I perform a 2d REAL to COMPLEX FFTW_ESTIMATE on both, resulting in two identical spectra of the ...
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0answers
125 views

Fourier transform and duality

Consider continuous even signals $x$ and $h$ with spectra $X$ and $H$. Now consider LTI system $L_1$ characterised by IMPULSE response $h$. When $x$ is the input in $L_1$, the output is $y_1$ with ...
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1answer
168 views

Octave: Poor performance of convolution by separable 1D kernels

As a newbie, I wrote a custom function in octave to perform a 2D image convolution using separable kernels. The results of this custom function were compared with conv2() and they were consistent. But ...
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1answer
3k views

Cross correlate a 2D array

I have a 2D array of eeg data with shape (64,512) - 64 electrodes, 512 timepoints I want to calculate the maximum cross correlation (irrespective of lag/time shift) between every single electrode, so ...
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0answers
86 views

What is the advantage of a convolution? [duplicate]

I was wondering what are the advantageous qualities of a convolution? Is it helping you find out how much of a signal correlates with another signal? Say you have two separate signals in the time ...
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3answers
1k views

Principal component analysis (PCA) on convolutional network features

Please, I have a question regarding PCA and features which are extracted from a convolutional layer. link if we have a test dataset , and we extract all conv features of all images at test dataset ...
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1answer
367 views

advantage of using impulse response function for LTI systems? [duplicate]

i have a discrete-time LTI system $L$ that takes input signal $x[n]$ and gives the output signal $y[n]$. since $L$ is LTI, $y[n]$ can be derived as a sum of shifted and scaled impulse responses of $L$....
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2answers
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Express circular convolution in terms of linear convolution

g[n], h[n] : finite length sequences of length 7 yC[n]: circular convolution yL[n]: linear convolution Express yC[n] in terms of yL[n]. If same two sequences of equal length are convolved using ...
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1answer
2k views

Recursive systematic convolutional code (RSC) realization in MATLAB

How can I implement $\rm RSC(2,1,2)$ in MATLAB? Can I use convenc function to build RSC? The convenc function has 2 arguments: ...
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2answers
1k views

Estimating the standard deviation of Gaussian filter from smoothed image

Firstly, let's say that in order to smooth an image, I convolve it with a Gaussian function having standard deviation $\sigma_x$ and $\sigma_y$. I am now interested in knowing if there exist methods ...
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1answer
133 views

Why do we not use square filters without windows? [duplicate]

This question may sound like "why do we use window functions", but it's not. So here it's: What we currently do: If we have a function $g(t)$ and its Fourier transform $G(f)$, and a window $W(f)$ and ...
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1answer
90 views

How to take the linear convolution of these two signals?

How do I perform the linear convolution of the following two signals? I am having trouble relating $x[n]$ to a series of points, like was given by $h[n]$ below. $$x[n] = e^{j\pi n}\left\{{u[n]}-u[n-...
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1answer
450 views

scipy.signal.decimate vs array operations

The following program generates a signal with a bit of noise according to some bits. I then try to decode the signal using convolve and decimate. 2 problems I notice: The whole this gets thrown out ...
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1answer
73 views

Convolution of $f(2x)$ and $g(3x)$

As I know, convolution is defined as $f(x)*g(x) = \int_{-\infty}^{+\infty}f(\tau)g(x-\tau)d_{\tau}$, but what if we want to convolve $f(2x)$ and $g(3x)$? It should be like $f(2x)*g(3x) = \int_{-\infty}...
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1answer
69 views

Interpretation of FIR output

I'm looking at the example for convolutions here, and I can't quite understand how the output of a FIR filter can be interpreted. Obviously, it's just the convolution of the impulse response and the ...
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1answer
4k views

2D Convolution as a Doubly Block Circulant Matrix Operating on a Vector

I was reading Fundamental Image Processing, Chapter 5 (Image Transforms), I encountered the following problem: Given the arrays $x_1(m,n)$ and $x_2(m,n)$ as follows: Write their convolution $x_3(m,n)...
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1answer
442 views

What is the total impulse response in a system with feedback interconnection?

Let's assume that we have a system with a typical feedback interconnection where the output is given by the following equation: $$y(t) = \left(x(t) - z(t)\right) \star h_{1}(t) \tag{1} $$ where: $$z(...
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2answers
3k views

How to prove a filter is separable?

I want to prove that 2D Gaussian filter is separable and we can separate it into two dimensions, my problem is about the size of filters. we should prove that $G(x,y)*I$(where $G(x,y)=$$\begin{bmatrix}...
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4answers
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Why is circular convolution used in DSP? Why not linear convolution?

Why are we using circular convolution in DSP? What's the main solid reason for the use of it in digital processing? Why does the concept of circular convolution come more often than linear ...
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0answers
237 views

Prediction-error filter for images

I am interested in studying local pixel value dependencies in images and I am wondering if it exists a general form of prediction-error convolutional filter that is able to suppress the image's ...
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1answer
927 views

Detecting zero-crossing in image filtered by Laplacian operator

This is my first question on this site, complete noob. But here goes. I have a positive Laplacian operator [[0,1,0], [1,-4,1], [0,1,0]] Now this Laplacian ...
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2answers
7k views

Convolution of two exponential signals

I'm a little new to signal processing and I'm trying to wrap my head around convolutions. I know the definition of convolution for a continuous signal is $$y(t) = x(t) * h(t) = \int_{-\infty}^{\...
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1answer
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Creating Periodic Impulse Train In MATLAB

If we multiply a Continuous-Time signal f(t) by a periodic pulse sequence we can get a sampled version of our signal. The problem I am having is that I am unsure how to create an impulse train in ...
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1answer
220 views

Convolution: generating a continuous-time signal from a discrete-time sequence

Given a discrete-time (DT) sequence $g[n]$, I want to represent it as a continuous-time (CT) signal. I can do this by representing this sequence as a weighted sum of Dirac delta impulses. Would it ...
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1answer
192 views

Beginner's question on LPF, Need for Sinc and windowing [duplicate]

As a student who has never constructed any real world DSP application, I am inclined to ask the following. Convolution in time domain is multiplication in frequency domain. For low pass filtering, ...
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1answer
305 views

How to derive $r(t) = c(t) \circledast \frac{1}{2} h_b(t, \tau)$?

Consider a linear time-variant channel. The transmitted signal is $x(t)$, the channel impulse response is $h(t, \tau)$, and the received signal is $y(t)$. Then $$ y(t) = \int_{-\infty}^\infty x(\tau) ...
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1answer
198 views

Implementing FIR with MATLAB

There are several ways that MATLAB implements FIR. One of them is that convolution function conv directly implements the convolution equation and if the input is ...
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3answers
674 views

Dynamic convolution vs Volterra series

I'm trying to understand how a dynamic convolution model relates to something like a Volterra series, and what kinds of effects the latter can capture that the former can't (and vice versa). By ...
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2answers
899 views

Convolving complex exponential with box function (discrete)

If I have $$x[n] = u[n] - u[n-4]$$ where $u[n]$ is the unit step function, and $$h[n] = e^{-i\frac{\pi}{2}n}$$ does $x[n] * h[n] = 0$? I tried doing the convolution sum and I got: $1 - i - 1 + i = ...
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2answers
664 views

Efficient computation of dot product of convolutions

I have two FIR filters $f_{1},f_{2}$ and two short time-slices of signals $s_{1},s_{2}$. I need to compute: $$\left<s_{1}*f_{1},\ s_{2}*f_{2}\right>$$ Which I compute using six FFTs: each $s_{i}...
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1answer
1k views

Filter : Spatial domain versus frequency domain

Note: This is a followup question of How can I create a custom band-pass filter?. Can you explain the following python source code?. Bandpass filter bank. Suppose, I have an equation ...