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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Convolution manually implement in Simulink

How to make block arrangements in Simulink to convolve 2 continuous input signal? For some reason, I have to be able to reset the convolution integral accumulation. Hence, I can't use the conv block ...
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Multiplication in frequency domain for a signal containing a whole frequency spectrum

Imagine we have two signals in the frequncy domain X(f) and H(f), for one of the signal H(f) I have the complex pair and the frequncy at which that complex pair exists. The second could be any random ...
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Constructing an input signal whose response is determined by the impulse response

I'm self-studying Signals and Systems by Alan Oppenheim, and I have some trouble understanding the solution to a homework problem. P5.13 tries to find the sufficient and necessary condition on the ...
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Convolution: graphing output y(t) with given input x(t) and impulse response h(t)

I have the following question in my mock exam. My graphing looks as following: Could someone please correct?
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Validity of taking an inverse $\mathcal{Z}-$ transform instead of taking an inverse DTFT

I have the following problem: I am using the Convolution Theorem and have got an expression of $H(z)X(z)$ and now I need to take $\text{DTFT}^{-1}(H(z)X(z))$, namely I have to take the inverse DTFT ...
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What methods allow learning "changes" in data, and then generating synthetic output?

Suppose I'm interested in a process of the sort: Original data -> Something happened to data -> Result data More particularly, consider that we observe many results of "something happened ...
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Convolution of infinite sums

We have $$ \sum_{n=-\infty}^{\infty}f(n) \sum_{m=-\infty}^{\infty}g(m) = \sum_{n=-\infty}^{\infty} \sum_{m=-\infty}^{\infty}g(m) f(n) $$ and $$ \int_{-\infty}^{\infty}f(x) dx \int_{-\infty}^{\infty}g(...
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Convolution of squares / boxcars

$$ \Pi(t/A) \star \Pi(t/B) $$ where $$ \Pi(t) = \begin{cases} 1,\ -1/2 \leq t \leq 1/2 \\ 0,\ \text{otherwise} \end{cases} $$ How to compute? Derivation/steps optional but welcome. Note: I'm aware of ...
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Convolve sinc trains

$$ \begin{align} & \mathrm{sinc}(As + .5)\sum_{n=-\infty}^{\infty} \delta (s - n/A)\ \star \\ & \mathrm{sinc}(Bs + .5)\sum_{n=-\infty}^{\infty} \delta (s - n/B) \end{align} $$ How to compute? ...
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Antenna pattern in frequency domain and Hamming window

I have an antenna pattern (azimuth cut) and I want to apply a Hamming window to it. In SAR processing the target is shaped by the azimuth antenna pattern, and on top of it it should be possible to ...
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What is the output signal's frequency when doing operations of two signals?

If I have two continuous time signals x(t) and y(t) of maximum frequencies Ω1, Ω2 respectively. I want to find the sampling frequency used used in continuous-discrete conversion of the following ...
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Labels in speaker verification

I'm a beginner. If I am using a Convolutional Neural Networks with Triplet Loss as a loss function (also combined with GAN and a Classifier) for building a model that performs Speaker Verification, ...
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Output of a LTI system [closed]

I'm trying to resolve this exercise but I don't even know where to start. Do I have to apply convolution? **It appears that this question is classified as homework - this an exame problem which I was/...
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Is there a relationship between the energies of the inputs to a convolution and the energy of its output?

I want to convolve discrete signals A and B. I can compute their energies beforehand by squaring the samples and summing the squares, but I'm curious if I can compute the energy of the signal I will ...
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3D Convolution with sum of multiple 2D Convolution operation

Probably this is a simple question, but I quite don't understand the reasons why I can replicate a 3D convolution operation with the sum of multiple 2D convolution operations. Is it a property of ...
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Convolution of a discrete signal using for loop problem

This is the specification of the LTI system with Input and response I have been asked to compute Convolution of the input and impulse using two for loops and evaluate the Input and Impulse Response ...
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Why do I need to shift time for getting a response?

Well this is a basic doubt. Let us take an example of a discrete time impulse response of a system as h[n] which has components at n= 0,1,2. Now my input signal is made of x[0]+x[1] I know the ...
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calculate discrete time signal convolution example by hand

Conv. is defined this way:$y[n] = \sum_{i=0}^\infty h[i]*x[n-i]$ I have this example: $x[n] =(3,-1,2,0,1)$ at sample times $n= (0,1,2,3,4)$ is the input of an LTI system with impulse response $h[n] = (...
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Impulse Response Formula

How can you determine the impulse response if you know the output of the system? You should change the input signal with the dirac function with the argument equal to $t$ or $t-\tau$? I have this ...
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Upsampling a non equally spaced signal [duplicate]

I have a signal that has not an equally spaced sampling time $T_s$, and I would like to upsample it with an equally spaced $T'_s$. My first approach was to interpolate it with a spline and then obtain ...
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Adjust Wavelet output to CNN

I want to extract features from the signal using DWT and then feed the results into CNN, after calling the 'dwt' library function I got a runtime error. ...
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Calculate power of sinusoids with FFT

Suppose we have a signal which contains several sinusoids with different known frequencies and noise. My object is to find the total power of these sinusoids. There are two methods for this problem, ...
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Reverse convolution

I was reading about linear systems and random processes and I came across this $$h_{k}*h_{-k}*rxx[k].$$ I know what convolution is and its formula. Does the minus sign affect both of the parameters in ...
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Advice on seperation of impulse responses for harmonic distortion orders

I am working based on Angelo Farinas paper: Simultaneous measurement of impulse response and distortion with a swept-sine technique. The purpose of the work is part of a loudspeaker measurement and ...
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Determine if the system is linear, time invariant

I have a system described by the following impulse response: $h(t,τ) = g(t-2τ)$ Where $g(t) = e^{-at}u(t)$ I have to determine if the system is linear time invariant causal Then I have to determine ...
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Determining whether a system is linear or not having the impulse response

I got many exercises where I have to determine the response of a system to an input signal The only things i have are the impulse response and the input signal. I was thinking I could use the ...
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Why is sweeping in convolution so confusing

From this formula, I thought that time constant (m or tau) is the variable sweeping from -infinity to infinity. But in this visualisation https://lpsa.swarthmore.edu/Convolution/CI.html, it is t the ...
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Signature for the kernels in fast-convolution

Continuing the discussion from Convolution kernel in Bluestein's algorithm it has a very specific signature of the kernel ...
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What is the Fourier convolution theorem range of application (example of Dirac comb times rectangular window)?

$\DeclareMathOperator{\sinc}{sinc}$ I have questions regarding the Fourier transform of the product of functions or distributions and the range of application of the convolution theorem. Context When ...
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Convolution kernel in Bluestein's algorithm

For any sequence zero-padding in one domain will result in interpolation in another domain and depending on center-padding or padding to right in one domain will either preserver or distort the phase ...
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Convolution between bit stream sampled by N number of samples per bit with a channel modeled as low pass filter

I generated a bit stream in MATLAB, from the transmitter to be convoluted by the channel I use MATLAB function "randi" between 0 & 1, so it generates random vectors of 0s & 1s and ...
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Convolution between a vector and another symmetric vector

Let's have the vector $y = h * x$ where $*$ is the convolution operation, $h$ is the channel with length $N$ and $x$ is a symmetry vector which means $x = [x_M, x_{M-1}, ....,x_0, 0 , x_0, x_1, .... ...
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The Matrix Form of a 2D Circular Convolution

I have 3 closely related questions regarding 2d convolutions and how they are represented in matrix form. 1. Miming what happens in 1d, I assume the product of a doubly block circulant matrix $A$ by a ...
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How are discrete convolutions applied to real world signals?

I'm in a position where I need to practically apply a filter to digitally sampled input data in realtime (from an ADC or otherwise). In other words, a Discrete Convolution. However, after reviewing ...
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What is edge-effect in discrete convolution?

My professor threw in the random term and never explained what it means cus he's been going on strike for 3 weeks straight.
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How to find the kernel of the convolution?

I'm trying to solve the following exercise: Image A was doubled by linear interpolation. The magnification was performed in two stages. In the first stage, add about zero pixel to the image between ...
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Proving Fourier transform of cosine multiplied with another function

Cheers, I have a impulse response that looks like this: $h(t) = h_1(t) \cdot \cos(8 \pi t)$ and I have to find its frequency response. In order to achieve this I am trying to use the fact that $$x(t)y(...
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how to prove that the convolution between two discrete signals is the discrete signal of convolution between two continuous signals

Like the title. We already know $x[n]$ and $h[n]$ are the discrete time signal of $x(t)$ and $h(t)$ respectively, which are continuous time signals. And also $x(t)*h(t)=y(t)$, $x[n]*h[n]=y[n]$. Prove ...
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How to zero pad and do overlapping block convolution to reconstruct audio for frequency filtering in time-frequency domain

I am doing STFT (short-time Fourier transform) on real-time audio to filter frequencies by magnitudes (to reduce noise) which have certain drawbacks like noise spikes in reconstructed audio in the ...
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1 vote
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Uniform partitioned convolution on a 2D image across height and width

I have 2D convolution with a large input image (512x1920). I am trying to partition the image across height and width to perform this convolution as N pieces. This would involve having an intersection ...
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Calculate output of exponential signal, given $H(\omega)$

Cheers, I am given the input signal of $x(t) = A \cos(2πft + \frac{\pi}{4})$ which is linear and time invariant, and I am asked to find the output, if I know that, $f = 500hz$ and $|H(f)| = 1, \angle ...
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3 votes
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Linear Time-Invariant system without State-space form

I would like to know whether there is any LTI system that does not have state-space representation, but do have a convolution representation. and vice-versa. Can you name some examples for me to ...
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Can multiple cross-correlation be expressed in terms of multiple Fourier transforms?

A post explains that the cross correlation of two signals can be given by $$\mathcal{F}^{-1} \left\{\mathcal{F}\left\{x(t) \right\} \mathcal{F}\left\{y(t) \right\}^* \right\}$$ Does this generalize to ...
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Ideal low pass filter with cut-off B does not affect a band-limited baseband signal with maximum frequency B

Let $x(t)$ be a band-limited signal with spectrum (fourier transform) lying between -B and +B. Such a signal is not warped by an ideal low-pass filter with cut-off frequency equal or higher than +B. ...
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Plot the sum frequency generation spectrum using convolution MATLAB

I am attempting to calculate the spectrum of a pulse that has undergone sum-frequency generation (in this case it is a gaussian, so it is correct to also say frequency doubling/Second harmonic ...
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What transformation preserves first term and averages the opposite conjugates?

I can't figure not find any reference on what is this transformation (what $X$ represents in relation to $A$). If $A=[a_1+jb_1, a_2+jb_2, a_3+jb_3, ..., a_n+jb_n]$, $X$ is defined as:$$X=\left[j b_1, \...
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5 votes
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Applying Convolution in Frequency Domain by Element Wise Multiplication on Time Domain

I'm studying the power spectrum. Right now, I am making a program to try to make sure that the "Fourier transform of the multiplication of some data and window function" and the "...
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Cumulative Distribution Function of 2-fold convolution

I'm looking for CDF of 2-fold convolution of $X$, with cdf: $F(x) = 0$ if $x < 0$ and $F(x) = 1 - ae^{-bx}$ if $x >= 0$ It looks like exponential, so I try somethings in here https://math....
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Why does convolution reverb work?

I've just begun learning about signal processing on my own, and after reading about convolution I'm curious about why convolution reverb works. That is given a recorded impulse $\hat{f}$ and an audio ...
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Does a FIR filter always perform a convolution operation?

I've come across this question in textbook. I guess it's basically asking are there any input or impulse response conditions that a FIR filter won't be able to compute. I can't think of any.
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