Convolution Definition and 338 Threads

I am having a hard time to understand why convolution integral gives the area overlaps of the two signal functions. if we use http://en.wikipedia.org/wiki/Convolution#mediaviewer/File:Comparison_convolution_correlation.svg for convolution, it is pretty obvious that one of the functions gives...

Homework Statement Find convolution of x[n] (graph in attachment) and h[n] where h[n] = u[n] Homework EquationsThe Attempt at a Solution - flipped the h[n] to have h[-n] - moved to the left once (h[-1-n]) to align - multiplied h and x and it gives me all zeros Is this correct or I'm missing...

Homework Statement [SIZE="5"] Find (use shortcut): x(t) = 2e-4tu(t) * e2tu(t) * t2σ(t - 2) Homework Equations Convolution properties: # "shape of Y (output) is different from x1, x2" # x1 * x2 = x2 * x1 # x1 * (x2 + x3) = (x1 * x2) + (x1 * x3) # x1(t) = * x2(t) * x3(t) * ... # step *...

Hi, New to this topic, and need some help. My task is to find the convolution between $ y= x ∗ h$ where $x = u_n - u_{n-N}$ and $h_n = u_n - u_{n-M}$ and $M\ge N$ are positive integers My understanding is that in general, $ y= x ∗ h = \sum\limits_{m=-\infty}^\infty x_m h_{n-m} $ so for my...

Hey, I've begun going through a book called "An introduction to geophysical exploration" by Phillip Kearey and Michael Brooks and I've come across a problem I can't for the life of me see how they got their answer. Essentially, given an input function gi (i = 1,2... m), and a convolution...

Hi, What is the derivative of a p-fold convolution? \frac{\partial}{\partial Y(\omega) } \underbrace{Y(\omega) * \dots * Y(\omega)}_{p-\text{times}} EDIT: I have two contradicting approaches - I guess both are wrong ;-) As a simple case, take the 2-fold convolution. FIRST approach...

A new variational principle is presented in this paper: http://arxiv.org/ftp/arxiv/papers/1112/1112.2286.pdf When trying to derive something like the equation of motion of a Duffing oscillator, I take the following approach: Set up the functional as such: $$...

Homework Statement Let FT(f) = Fourier transform of f, (f*g)(x) = convolution of f and g. Given FT(f*g) = FT(f)FT(g), the first part of the convolution theorem, show that FT[fg] = [FT(f)*FT(g)]/2pi. Homework Equations Duality: FT2f(x) = (2pi)f(-x) Convolution: (f*g)(x) =...

I tryied make the convolution product between x² and x³ by ##\int_{- \infty}^{+ \infty} f(u) g(x-u) du## and the result is an indeterminate form, however, by defintion ##\int_{0}^{x} f(u) g(x-u) du##, the result is 1/60 x6. So, \int_{- \infty}^{+ \infty} f(u) g(x-u) du \overset{?}{=}...

Hi All, I am taking Dynamic Systems and Controls this semester for Mechanical Engineering. We are solving non homogeneous state space equations right now. This question is about a 2x2 state space differential equation that takes the form: Where A and B are matrices, while u is an input...

Hi, I have the following problem: Let x,y be finite real valued sequences defined on 0...N-1 and let g be a non negative integer . define also on 0..N-1. In addition, the DFT of y is known in closed form. Is there a way to write z as some cyclic convolution, so that with the...

Let x,y be finite real valued sequences defined on 0...N-1 and let g be a non negative integer . define also on 0..N-1. In addition, the DFT of y is known in closed form. Is there a way to write z as some cyclic convolution, so that with the help of the convolution theorem z can be calculated...

Hello, given two functions f and g the operation of convolution f\ast g finds many applications in many different branches of science. However, in such applications, it is typically assumed that one of the two functions (the convolution kernel) is a real scalar field, although the mathematical...

Homework Statement (f*g)(x) = integral from -pi to pi of (f(y)g(x-y))dy f(x) = ∑cneinx g(x) = ∑dneinx en is defined as the Fourier Coefficients for (f*g) {the convolution} an is denoted by: en = 1/(2pi) integral from -pi to pi of (f*g)e-inx dx Evaluate en in terms of cn and dn...

Ok so I've seen the convolution theorem written as: F(h(x)\otimesg(x))=H(k)G(k) (And this is how it appears when I have a quick google). My book then does a problem in which is uses: F(h(x)g(x))=H(k)\otimesG(k) Where H(k)=F(h(x)) and similarly G(k)=F(g(x)), and F represents a Fourier...

It is known that:\mathcal{F}\{f\ast g\}=\mathcal{F}\{f\}\mathcal{F}\{g\}\mathcal{F}\{f g\}=\mathcal{F}\{f\}\mathcal\ast{F}\{g\} But this property is valid for inverse tranform too?\mathcal{F}^{-1}\{F\ast G\}=\mathcal{F}^{-1}\{F\} \mathcal{F}^{-1}\{G\}\mathcal{F}^{-1}\{F...

Okay the question is to find the Fourier transform of: rect(\frac{x}{5})\otimes(\delta(x+3)-\delta(x-3)) =F^{\infty}_{\infty} \intrect(\frac{x'}{5})(\delta(x+3-x')-\delta(x-3-x')) dx' [1] - where F represents a Fourier transform. My Issue Okay I am fine doing this using the convolution...

Let us write a convolution $$\int_{0}^{t} A(t-\tau) \mathrm{d}x(\tau)$$ as $$A \star \mathrm{d}x$$ I would like to write down the expression for the double convolution $$A \star \mathrm{d}x \star \mathrm{d}x $$ Following the definition I obtain $$ \int_{0}^{t} \int_{0} ^{t-\tau}...

Hi all I was wondering if someone could have a look at my answer attempts. I am having great trouble with Q.3 so any help would be greatly appreciated. Figures are attached Homework Statement Q1. Sketch expected image profile for rectangular protrusion from an otherwise locally flat...

Homework Statement Part (a): Find the intensity as function of ##\theta## and sketch it. Part (b): Find the intensity as function of ##\theta## and sketch it. Comment on first minima. Homework Equations The Attempt at a Solution Part(a) Convolution Method V_b = \frac{1}{2a}, 0 \leq...

Hi everyone, I want to calculate the convolution of two triangluar pulses Homework Statement both functions are given by x(t)=\left\{\begin{array}{ll} t+1, & -1 \leq t \leq 0 \\ 1-t, & 0 \leq t \leq 1 \end{array}\right. and I rewrote the other as h(-t+t) Homework...

Homework Statement Part(a)/(b)/(c): Fourier transform the following: Part(d): Prove the convolution theorem Part (e): Find total displacement Homework Equations The Attempt at a Solution Part(a) f = \frac {1}{sqrt{2\pi}} \int_{-\infty}{\infty} F e^{-iωt} dω \frac {1}{\sqrt{2\pi}}...

Hello, I am trying to numerically evaluate a convolution integral of two functions (f*g) using Fourier transform (FT) i.e using FT(f*g) = FT(f) multiplied by FT(g) (1) I am testing for a known case first. I have taken the gaussian functions (eq. 5, 6 and 7) as given in...

Hello all, I am currently working on studying for my P actuary exam and had some questions regarding using convolution for the continuous case of the sum of two independent random variables. I have no problem with the actual integration, but what is troubling me is finding the bounds...

Hi everyone Homework Statement I want to to calculate the convolution of the following two functions h(t)=\left\{\begin{array}{ll} t, & 0 \leq t \leq 10 \\ 0, & otherwise\end{array}\right. and the function x(t)=\left\{\begin{array}{ll} A, & 0 \leq t \leq 10 \\ 0, &...

Hello all, What is the result of this (linear) convolution: s(t)\star\delta(\tau-\tau_p) where s(t) is a continuous signal, δ is the Dirac delta function, and \tau_p is a constant. Thanks in advance

x_1(n) = (!/4)^n u(n-1) and x_2(n) = [1- (1/2)^n] u(n) X_1(z) = (1/4)z^-1 / (1-(!/4)z^-1 and X_2(z) = 1/(1-z^-1) + 1/(1-(1/2)z^-1) Y(z) = X_1(z) X_2(z) = (-4/3) /(1-(1/4)z^-1 + (1/3) / (1-z^-1) + 1/(1-(1/2)z^-1

Homework Statement Determine the Laplace Transform of ∫(from 0 to t) (t-τ)cos(2(t-τ))e-4τ dτ using Laplace Transform tables. Homework Equations I know the basic convolution theorem is (f*g)(t) = ∫f(τ)g(t-τ)dτ The Attempt at a Solution I'm not sure if this is double convolution...

I'm in class watching my professor teaching us about convolution. However, he keeps doing this by creating graphs and stuff. Is there a method through which I can solve convolution problems without having to draw the graphs?

Homework Statement I need to find the laplace transformation of the following function (and it's ok to leave it expressed as an integral). After doing the initial steps and algebra I got Y(s)= g(t)/(s+2)^2 + 7(1/(s+2)^2)+ 2(1/(s+2)^2) the answer is y(t)=2e^-2t +te^-2t...

Homework Statement How do I prove that sinc(t) * sinc(t) = sinc(t)? Homework Equations The Attempt at a Solution I converted it to frequency domain and got that rect(f) rect (f) = rect (f) which then converts back to sinc (t). But I'm just curious as how would I go about doing...

Hello, I have really been banging my head the whole day and trying to figure this derivative out. I have a function of the following form: F = W * (I.J(t)) - (W * I).(W*J(t)) where I and J are two images. J depends on some transformation parameters t and W is a gaussian kernel with some fixed...

Hi all, I have an all time doubt here. We know that if r.v z = x + y where x and y are 2 random sequences having corresponding pdfs p(x) and p(y), the pdf of z, p(z) = convolution ( p(x),p(y) ). I have seen the derivation for the continuous case although not thorough how to prove it. I...

Homework Statement You have two functions in Matlab (represented as column vectors). Compute their convolution using the fast Fourier transform. Homework Equations The Attempt at a Solution I am having trouble finding a book with this topic. I would like to know where the...

Homework Statement The unit impulse response of an LTIC system is h(t) = e^{-t}u(t). Find the system's (zero-state) response y(t) if the input f(t) is e^{-2t}u(t-3). Homework Equations y(t) = f(t) * h(t) = ∫^{∞}_{-∞}f(t)h(t-\tau)d\tau f_{1}(t) * f_{2}(t ) = c(t) f_{1}(t) * f_{2}(t - T) =...

Hi, y(t) is the response of LTI system A to x(t). How could I have figured out that y(t) = x(t) - x(t-2a) (please see attachment). By looking at the graphs this isn't apparent to me :S.

Hi, I have a question concerning convolution. I don't quite understand the boundaries of the integration in the attachment. The way I see it, the areas do not overlap at all for 1<t<3. You might say that they do overlap at 0, but that is usually not considered an overlap. Even if they were...

Homework Statement Prove that the convolution of e^{-\left|x\right|} is (1-x)e^{x} for x<0 and (1+x)e^{-x} for x>0 Homework Equations The Attempt at a Solution I plug through the integral in the standard way and take the limits as x tends to positive and negative infinity etc...

please anyone can help me to get the answer?I have idea about aliasing which is basically in frequency domain caused by lower sampling rate which does not satisfy the Nyquist criteria. Frequency aliasing refers to higher frequency getting the image of lower frequency.But what is time domain...

What's the difference between convolution and crosscorrelation? I read the answer below, but I don't know enough math to understand it. Could someone clarify it for me, please? "The meaning is quite different. To see why in a simple setting, consider X and Y independent integer valued...

So I am looking for some insight one how I might go about solving this problem. I have two equations f and g where f = g = \frac{1}{(1+x^2)}. The convolution theorem states that L(f*g) = L(f)*L(g) where L can be either the Laplace transform or the Fourier transform. So it will look like this...

I am really confused where to start with this problem. I know about convolutions somewhat. We have done them a little. Where is a good place to begin with this problem?

Hello, I'm having some trouble understanding the concept of two function convolution in Fraunhofer diffraction. Let's say I have an aperture function in the shape of some cosine function (which is always above zero), and I want to calculate the transmission function if I only illuminate 3...

Hello, Consider I have a linear time-invariant (LTI) system, with ##x(t)##, ##y(t)##, and ##h(t)##, as input, output, and impulse response functions, respectively. I have two choices to write the convolution integral to get ##y(t)##: $$ 1)\ \ \ y(t) = \int_{0}^{t} h(t-t')x(t')dt' $$ and...

How would you interpretate this image about LTI systems and convolution?

Hello all, I am having some trouble calculating a convolution. For the question, and my attempt at a solution, please take a look at the pic. Can someone please point me in the right direction?

Boas Ch. 8, Sec. 10 #3 Use the convolution integral to find the inverse transforms of: \frac{p}{(p^{2}-1)^{2}} = \frac{p}{p^{2}-1} \frac{1}{p^{2}-1} I'm completely confused with these things. Are we supposed to figure out the inverse Laplace transform and then use that within our convolution...

I have given the question and my attempt in the image that i have loaded please tell me that am i doing it right ?

Hi PF, What is circular convolution? Why do we need such an operation if we have linear convolution, What is its basic difference of both convolutions. Is circular convolution used only in frequency domain? -Devanand T

Homework Statement Compute the convolution y[n] = x[n] * h[n] if discrete signals: x[n] = \alpha^nu[n] h[n] = \beta^nu[n] Where \alpha \neq \beta. Homework Equations y[n] = \sum_{k=-\infty}^{\infty} h[n-k]x[k] The Attempt at a Solution I plugged the two equations into...