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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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1answer
93 views

Reduce signal size to compare them

I have multiple experiments and each of them produce several ($k$ for example) binary signals; some artificial example next: I have a metric to compare experiment results but I need vectors of equal ...
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1answer
2k views

Implementing Frequency Domain Convolution in MATLAB (Convolution Theorem)

I'm trying to prove convolution in time domain is same as multiplication in frequency domain but I'm not getting the same answer in matlab. Here is the code:
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376 views

Minimal number of additions in convolution

The Winnograd algorithm can be used to reduce the number of multiplications in convolution. Is there a known method of reducing the number of additions in convolution?
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1answer
389 views

PDF of a sum of two RVs by convolution of their samples via fourier transform in Excel

I apologies if this is off topic for this site, but I am trying to figure out (and not having much luck) how to get an empirical distribution function of a sum of two random variables given two ...
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0answers
68 views

How to convert multi-band Energy Time Curve (ETC) to Impulse Response (IR)?

I am running my own sound simulator. Now I have obtained the Energy Time Curve (ETC, expressed by energy) by physical simulation, and they are stored in 8 discrete frequency bands (because decay of ...
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1answer
127 views

2D image convolution: when to peform direct convolution and when to perform FFT/multiple/IFFT

I want to convolve 2 images I1 and I2. Let's assume they have the same size. I know 2 methods: 1) Use direct definition of 2D convolution 2) i. Computer FFT of I1 (call it I1_FFT) and FFT of I2 (call ...
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1answer
226 views

3D FFT's and Convolutions using FFTW

I am trying to perform a of convolution 2 3-dimensional vectors using the FFTW3 library in C. My question relates to the order in which the frequency domain appears and if it will make a difference ...
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62 views

Convolution of shifted in time signal

$$X(t)\star Y(at-b)=\int_{-\infty}^{\infty}X(\tau)Y(a(t-\tau)-b) \; d\tau = \int_{-\infty}^{\infty}Y(a\tau-b)X(t-\tau) \; d\tau $$ My question - is this correct? (let's say $a \ne \{0,1\}$ )
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Applying phone-effect on clean speech corpus without spectogram loss

I intend to train an end to end speech recognition engine for phone conversations. Most of the available corpus is crystal clear narrated data, so i'm looking for a way to bring my training data ...
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0answers
81 views

How to reconstruct/resample/interpolate a 3D signal using convolution

Assuming we have a sampled 1D signal and we want to upsample/resample, then we add 0 values inbetween the existing samples and then do convolution with a reconstruction filter e.g. $H(s) = [0.5, 1, 0....
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5answers
424 views

Fast & accurate convolution algorithm (like FFT) for high dynamic range?

It seems that FFT-based convolution suffers from limited floating-point resolution due to evaluating everything around the roots of unity, as you can see in the $10^{14}$-factor error in this Python ...
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2answers
102 views

Would anyone be able to help out with the following discrete convolution question?

I have been trying to attempt this question for quite a while and I am not sure how to approach it. Would anyone be able to help out with the working?
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1answer
60 views

Convolution a 3-D signal with 2-D signal

I have a 3D signal $M(x,y,t)$ and I want to do convolution with signal $G(x,y)$ and $Et(t)$, I mean, how to calculate this Convolution below in Matlab? $$A(x,y,t)=M(x,y,t) \star G(x,y) \star Et(t)$$ ...
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2answers
571 views

Solving a Convolution Problem

I was unable to solve a convolution question.Question is attached herewith. I don't know how to initiate for solving the problem and what is the final expression that prove the convolution of a top-...
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1answer
26 views

measuring how much signal corrupted by passing from a medium [closed]

I am looking for a measure to report how much a signal has corrupted by passing a medium. Suppose we have a signal 2Hz and amplitude ...
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1answer
145 views

Filter design to realize Cauchy product

I come from Computer Science so please pardon for my possibly wrong terminology. I need to design a filter which has coefficients $$h_0, h_1, \ldots, h_n, \ldots \quad\text{such that}\quad h_0 > ...
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0answers
22 views

Recognize irregular repetition of unknown feature (stamps at random locations)

I have an image which is generated by convolution between (1) a simple small patch and (2) larger image composed of localized point-like features (e.g. slat-and-pepper noise, sum of shifted $\delta$-...
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2answers
277 views

Two real time signals convolving

This might be a stupid question but is it possible to convolve two real-time signals together? I know that generally for running convolution you have the IR and the block of the real time signal and ...
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1answer
46 views

Deep learning model for phone recognition - issues with dimension the model

I seem to have some problems understandind how the model described in this paper has been designed This is what is written about the model dimension.. ...In these experiments we used one ...
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1answer
116 views

Is sampling a Fourier transformed signal and fourier transforming a sampled signal the same?

I'm having a hard time understanding an assignment that states: Draw the complex spectrum of the sampled signal $f(t)$ (periodic and continuous). Do this, by first calculating the Fourier ...
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2answers
561 views

Implementing a Band-Pass Filter from Scratch

I am trying to implement a band-pass filter from scratch. Here is an article which I thought explained the nuts and bolts of how to build one; the author combines a low-pass with a high-pass filter (...
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2answers
1k views

Parameters of Gaussian Kernel in the Context of Image Convolution

Hi Everyone i am new at image processing. I copy code from this website, I have image $600 \times 480$ gray scale. What will be the value of standard deviation or $\sigma$? What will be the value of ...
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0answers
166 views

Applying a frequency filter in dB onto an audio wav file in the frequency domain

I am working on a university project consisting of a C program supposed to apply a correction of the isophonic curves to an audio PCM file. So far, I have managed to code the most part of it (read/...
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1answer
402 views

Prewitt operator and central difference?

When taking the gradient of an image one can do $I * \begin{bmatrix}+1 \ 0 \ -1\end{bmatrix}$ (x direction). As I understand this is basically applying central differences in the x direction, $\...
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0answers
80 views

Fastest way to subtract known music tracks from live videogame audio stream

I want to isolate video game "action" sounds from the video game soundtrack. Given all ~20 songs, I'd like to filter them out from any live audio stream during gameplay. What is a fast and robust way ...
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3answers
1k views

Convolution and Deconvolution in C

I understand the theoretical foundations of convolution, but now that I'm trying to program it I'm having some issues conceptually. Say I have two blocks of 64 audio samples each. I also have access ...
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1answer
260 views

Filtering White Noise to Generate Harmonic Signal

I have studied convolutions and filters a long time ago. Today, I am trying to review the basics using some notes of mine, but I am finding difficult to solve easy problems. Since I don't have ...
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1answer
385 views

How to do convolution a 2D signal (some image) and result of convolution of two 1D filters?

Assume a 2-D signal (i.e., some image). Load image and assume it to be signal x. Next assume that instead of having a 2-D filter you have two one D filters $$f_1[n] =\begin{bmatrix}0.25 && 0....
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2answers
85 views

Overall system IR: How to do arithmetic with $\delta$ functions?

When finding the overall system impulse, how to do arithmetic with $\delta$ functions? E.g. \begin{align} h[n]&=h_1[n]\star h_2[n]\\ &=\sum_{k=-\infty}^{\infty} h_1[k]h_2[n-k]\\ &=\sum_{...
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1answer
95 views

Understanding an alternative representation for the difference equation of a FIR filter?

I recently solved a problem which required that I compute the convolution of an input signal with the impulse response of a filter. I got the resulting discrete signal which is verified to be the ...
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0answers
225 views

Deconvolve using divsion of FFT of shifted signal in time domain

I have FFT of two signals. Y=120 , Y1=80 Hz. to convolve in time domain I can convolve them using their ffts. as ...
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2answers
547 views

Using convolution as feature extraction?

I am now studying image processing in my spare time. My understanding of convolution is about 'response to a specific filter': When we have a raw image, or raw signal; and a filter, aka kernel; we ...
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2answers
659 views

Why does reversing the order of these two transfer functions give me different outputs?

Consider these two systems: \begin{align} &u\ {\longrightarrow}\boxed{s}{\longrightarrow}{\boxed{\frac 1s}}{\longrightarrow}\ y\\ &u\ {\longrightarrow}\boxed{\frac 1s}{\longrightarrow}{\boxed{...
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1answer
570 views

Is periodic convolution same as circular convolution?

I know exactly what is periodic convolution. But i don't know if circular convolution means to be the same thing!
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1answer
842 views

Convolution of Two Kernels [OpenCV]

I've been completely stuck on a portion of my assignment for a few days now. After plenty of searching around, I have been unsuccessful in discovering information that leads me to the correct solution....
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1answer
684 views

How to implement the $\tt conv(x,h)$ in MATLAB without using loop?

I'm trying to calculate convolution of two given vectors in MATLAB without using loop, and of course without the function conv itself, but I can't remove the last ...
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2answers
726 views

Convolution of two large signals in MATLAB

I need help regarding convolution. I am trying to convolve a signal which is $15\textrm{ ms}$ long, and the sampling frequency is $10\textrm{ GHz}$. I need to convolve it with a rectangular pulse, ...
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0answers
31 views

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
90 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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1answer
437 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
323 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
338 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
273 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
153 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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2answers
9k views

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
87 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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0answers
205 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
351 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 ...