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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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Can this robot trajectory smoothing function be expressed as a single convolution?

I have an Nx3 matrix of poses (x, y, theta) that I need to apply an algorithm on which will cause the trajectory to be smoothed. I am interested in performance and so would like to improve efficiency ...
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1answer
93 views

Delayed impulse does not delay spectral response

Inspired by Dr. Sarwate's answer to the question How replicas are formed in Frequency domain when a signal is sampled in Time Domain? , I decided to see for myself the underlying concept. I ...
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486 views

Comparing band-pass filters and convolutional kernels?

I am currently working on extracting features for speech recognition purposes. I wanted to try an approach similar to MFCC features in which the center frequency of each band pass filters are placed ...
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1answer
364 views

Time-spread multiple echoing of audio signals

I have been reading papers related to adding echos into digital audio signals recently. I guess I understood the logic behind, yet I guess I am still having lack of DSP knowledge to figure out ...
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1answer
377 views

Fourier convolution of a histogram

Notation: $\mathcal F\left\{a\right\}$ denotes applying the discrete forward Fourier transform to the histogram $a$. Similarly for $\mathcal F^{-1}\left\{a\right\}$ and the discrete inverse Fourier ...
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1answer
285 views

Control systems and convolution

I think i am not understanding the concept of convolution well. Lets say we are given a system impulse response in the S-domain, and we have implemented a controller $G_c(s)$ that will adjust the ...
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2answers
157 views

Why do we assume zero mean noise in sensor data?

I am reading a paper on measuring respiratory patterns from video data. In defining the model, the authors formulate the problem mathematically as: $x_i(t)=h_i(t) \ast g(t) + n_i(t) $ Where $n_i(t)...
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What is the difference between Difference of Gaussian, Laplace of Gaussian, and Mexican Hat wavelet?

There are three techniques used in CV that seem very similar to each other, but with subtle differences: Laplacian of Gaussian: $\nabla^2\left[g(x,y,t)\ast f(x,y)\right]$ Difference of Gaussians: $ \...
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2answers
95 views

change convolution function if signal is above threshold?

Let's say I have a signal $s(t)$ and two filters $f_1(t)$ and $f_2(t)$, I also have a threshold $A$. Now I define $a_1(t)$ as $a_1(t) = \min(s(t),A)$, then I do the convolution of $a_1* f_1$. Now I ...
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1answer
87 views

Does anyone can help me with signal processing problem?

(c)A linear time-invariant system with impulse response $h(t)=e^{-\alpha t} u(t)$ is driven by the input $x(t)=e^{-\beta t} u(t)$ . It is assumed that $\alpha, \beta > 0$. (i) Using ...
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234 views

Proper way of representing Static, delta, delta delta in a plot

I am currently working on recreating the result of this paper. The paper is about applying cnn in speech recognition, in which cnn is used to for feature extraction, for which a proper way of ...
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1answer
2k views

conversion of 1d signal to 2d signal for CNN operation

I have a 1D signal data sampled at 25kHz and I want to modify in to 2D signal so as to modify it as the input to ConvolutionalNets as they work only on 2 dimensional data. What are possible ways to ...
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1answer
375 views

Fourier transform of Kernel Density estimate: convolution theorem?

I am reading this paper about density estimation (Appendix A), where the authors apply a Fourier transform to the estimated probability density (the $X_j$ are a sample of $N$ data points drawn ...
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2answers
3k views

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
155 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
247 views

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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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
145 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
249 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
280 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
54 views

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
132 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
380 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
129 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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3answers
982 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
4k views

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
1k views

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
497 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
90 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
382 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
55 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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60 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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1answer
187 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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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
428 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
144 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
95 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
512 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
77 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
74 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
472 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
4k views

How to Prove a 2D 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
17k views

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
246 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
1k 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 ...