Convolution Definition and 364 Threads

Hi, Can anyone tell me if there is a convolution theorem for the Fourier transform of: \int^{t}_{0}f(t-\tau)g(\tau)d\tau I know the convolution theorem for the Fourier Transform of: \int^{\infty}_{-\infty}f(t-\tau)g(\tau)d\tau But I can't seem to find (or proove!) anything...

Homework Statement Calculate the discrete time convolution y[n] = x[n] * h[n] , where x[n]=(1/2)-nu[-n-1] is the input h[n]=u[n] is the impulse responseHomework Equations Discrete time Convolution formula, where x[n] is the input and h[n] the impulse response...

If one has input x(t), then convolving x(t) with impulse response of the system would give the zero-state of the system. For example, we have a system described as : (D^{2} + 4D + 3)y(t) = (D+5)f(t). I computed system impulse response which is : h(t) = 2e^{-t} - e^{-3t} Now if say f(t) =...

Homework Statement H = X + Y where X and Y are two continuous, dependent random variables. The Joint PDF f(x,y) is continuous. All the literature that I have looked at concerning this matter have dealt with the convolution of two independent random variables. Homework Equations All I know...

Homework Statement x'' + 2\zeta \omega_{n} x' + \omega_{n}^2 x = u_{s}(t) zeta is underdamped and u_{s}(t) is the unit step function and \omega_n is the natural frequency and there are zero initial conditions. Find the total response via the convolution integral. Homework...

Hello everyone, I have a quick theoretical question regarding probability. If you answer, I would appreciate it if you would be as precise as possible about terminology. Here is the problem: I'm working on some physics problems that do probability in abstract spaces and the author freely...

Homework Statement Can someone please help me. I have finish the problem but i don't know if its right. Can someone please check my answer. I'm attaching it as a PDF and Its for my EE signals and systems class and the book we are using is signals and systems by Alan V. Oppenheim Homework...

Will we get a high frequency signal from convolving 2 high frequency signals? Also will we get a low frequency signal from convolving 2 low frequency signals? How about convolving one low and one high frequency signal? My intuition tells me its low frequency signal. Thanks for any...

I had a terrible adjunct professor in ODEs and got little or no theory. I'm not in PDEs and my much better professor just (re)introduced convolutions while generalizing the heat equation to Rn - unfortunately it was not a reintroduction for me. Later chapters in the book deal with...

Not a specific question per se but... Is it possible to convolve a discrete-time signal with a continuous-time one? if you have x(n) and y(t) can you calculate the convolution of x and y (say, by taking y(t) for t in the set of integers or by treating each x(n) as its value multiplied by...

I am a little confused about convolutions. I know that convolution is the multiplication and then integral of the two signals. The confusion starts at the commutative property. If i try to change the time-shift from signal to another for any 2 general functions or equations the commutative...

Homework Statement x(t) = u(t) - 2*u(t-2) + u(t-5) h(t) = exp(2*t) * u(1-t) Homework Equations Need to find convolution integrals for all possible intervals The Attempt at a Solution Ok, the first thing to do is to rewrite these equations in terms of \tau. Now i have: x(\tau) =...

The operators act on a vector to produce another vector. They are matrices, therefore. For instance, the backward shift (aka delay) operator, z, acting on vector, say y, translates k-th element into k-1-th: zyk = yk-1. It is normally z-1 in z-transform but I will ignore the difference where it...

Hi there, I'm having trouble convolving two signals, according to this site "http://cnx.org/content/m11541/latest/" " and its example, for the time period 0≤t<1 they've used the integral yt=∫dτ between 0≤t<1. My problem is, how did they get this integral?. I get that the height of the two...

How do I compute convolution of exp(-a*norm(x)^2) and exp(-b*norm(x)^2) where a,b > 0 and x belongs to Rn? I wonder if there is an easy way to compute this convolution using Fourier transform.

Hello, I want to do the convolution of a gaussian function and a hole. If I want to use Fourier transform which functions should I use? Can I use rms? I want to calculate the spot size of a gaussian signal after a circular aperture. Thanks!

cant understand the red arrow transition i changes the intervals and i cuts half of the arguent inside the integral i can't see why ? regarding the interval change the H function is 1 in a certain interval so if they change the integrval then its no longer H inside because we have taken...

cant understand the red arrow transition i changes the intervals and i cuts half of the arguent inside the integral i can't see why ? regarding the interval change the H function is 1 in a certain interval so if they change the integrval then its no longer H inside because we have taken...

The latex code here is doing all sorts of odd things... :( ... anyway, The convolution algebra is l_1(\mathbb{Z},\mathbb{C}), the set of functions f:\mathbb{Z}\rightarrow\mathbb{C} which satisfy ||f||:=\sum_{n=-\infty}^{\infty}|f(n)|<\infty with pointwise addition and scalar...

Hi, can someone please give me an example of what a convolution of a convolution would look like ? Thanks

So I wanted to find the convolution of two monomials (don't ask me why) in the most general way I knew how. Of course, I only knew how for positive integer powers, but maybe someone can tell me how to do it for positive real powers (Gamma function maybe?). Anyway, here's what I did, replacing...

Derivative of a Convolution Homework Statement How do I find the derivative of a convolution, meaning \frac{d}{dt}(f \ast g)(t)? Homework Equations (f \ast g)(t)=\int^{}_{} f(t-\tau)g(\tau)d\tau The Attempt at a Solution I want to use the fundamental theorem of calculus, but I...

Again, in my quest to learn things I won't use in a class for at least a year, I've been looking at convolutions. Specifically, after finishing the multiple choice section of an AP Chemistry test 50 minutes early, I looked at the convolution of a polynomial with itself. I'm confused about one...

Homework Statement Let f,g be two continuous, periodic functions bounded by [-\pi,\pi] Define the convolution of f and g by (f*g)(u)=(\frac{-1}{2\pi})\int_{-\pi}^{\pi}f(t)g(t-u)dt. Show that (f*g)(u)=(g*f)(u) The Attempt at a Solution I think the way I'm...

The answer doesn't seem obvious to me: If I set up B_0 = 1 and B_n = n^2 Then let A_n = \sum_{m=0}^n B_m B_{n-m} = 2B_0 B_{n} + 2B_1 B_{n-1} + \ldots Then I almost expected A_n to grow like n^2. Instead, I'm getting (numerically) that A_n \sim O(n^5)! Why is that? In general, it seems that...

Homework Statement I(x) is the intensity of an image after passing through a material which blurs each point according to a point spread function given by: S\left(x'-x\right)=e^{-a\left|x'-x\right|} The Fourier transform of I(x) is given by: I(k) = \frac{A}{\left( a^{2}+k^{2}...

Homework Statement x(n)=u(n); h(n)=(0.5)^n; y(n)=x(n)*h(n); find y(n) Homework Equations The Attempt at a Solution thank you

In Apostol's "Mathematical Analysis", Page 328 (see the image below and the underlined sentence), why does the Lebesgue integral (41) exist for ?[/URL] The definition of convolution is as follows: Thanks!

I'm trying to do FFT convolution via the FFTW3 library for image processing purposes. Basically I have a kernel and I am convolving it with an image. A problem I encountered has to do with the dimensions of the image. When the width is not equal to the height, the pixel values I get, seem to...

Here is convolution: c[k]= (0.5)^k * delta(k-1) What do I do about delta(k-1)? I know if it is c[k]= (0.5)^k * delta(k), then it just equal (0.5)^k But what do I do with delta(k-1)?

Hi everyone, I uploaded a solution about Fourier transform. At the solution of this problem, it states that make convolution. But i tried to do convolution but my result is not same with this result. When you do the convolution with 2.10 and 2.11, is the result 2.13 correct ? How is it done ...

Dear Experts, For convolution to work any input signal we should be able to represent the input signal in terms of appropriately scaled and shifted unit impulses. This one holds good for discrete time system in which the input signal can be represented as sum of scaled shifted...

P_r is defined as: P_r(x)=\frac{1-r^2}{1-2r\cos x +r^2} and P_r(x)=\frac{1-r^2}{1-2r\cos x +r^2}=\sum_{n=-\infty}^{\infty}r{|n|}e^{inx} and f(x)=\sum_{-\infty}^{\infty}c_ne^{inx} which is continues i need to prove that...

Hello, If f is a morphism between two vector spaces, we say it is linear if we have: 1) f(x+y) = f(x) + f(y) 2) f(ax) = af(x) Now, if f is the convolution operator \ast , we have a binary operation, because convolution is only defined between two functions. Can we still talk about linearity in...

I will make this my discussion thread. I have many questions to ask which I will post here. Please keep checking. All help will be appreciated. My first question is: For discrete signal, we use variable 'n' and for continuous signal, we use variable 't'. But is the convolution integral valid...

Homework Statement Hi, can anyone help me to determine the convolution for the 2π periodic function f(t)=e^t and sin2t

Homework Statement u(t) * u(t) * u(t) * indicates convolution Homework Equations i know u(t) * u(t) = t u(t) The Attempt at a Solution so (t u(t)) * u(t) = \int \tau d \tau limits of integration are 0 to t so the answer is 1/2 t^2 u(t)?

I need to find the convolution product f*g when the functions f, g on P_{4} are given by: (a) f:=(1,2,3,4), g:=(1,0,0,0) (b) f:=(1,2,3,4), g:=(0,0,1,0) I know that (f*g)[n]=f[0]\cdot g[n]+f[1]\cdot g[n-1]+f[2]\cdot g[n-2]+...+f[N-1]\cdot g[n-(N-1)] and \sum_{m=0}^{N-1}f[m]g[n-m] when f...

Greetings, I am a computer scientist revisiting integration after a long time. I am stuck with this simple-looking integral that's turning out to be quite painful (to me). I was wondering if one of you could help. The goal is to solve the integral \int_{0}^{\infty} e^{-(x - t)^2/2...

Hello. I need help with understanding one part of the convolution procedure. This doesn't involve any particular homework problem, but I'll use the following problem as an example: http://img34.imageshack.us/i/tempuf.jpg/ I have 2 questions. If anybody can help me, I would greatly...

Homework Statement y(t) = \int ^{t}_{-\infty} e^{-(t-\tau)} x(\tau-2)d\tau Find h(t), given that the continuous time linear time invariant signal has input x(t) and output y(t). 2. The attempt at a solution I was wondering if I can simply manipulate the expression until i get it in the...

(f*g)=\int_{-\infty}^{+\infty}f(\tau)g(t-\tau) i was told that because of the definition of the function we can substitute the itervals to (f*g)=\int_{0}^{t}f(\tau)g(t-\tau) why??

So I have some problems and I tried to resolve them, I also have the results so I can check them but I'm curious if I made them good. P1: (H*δ)'=?, where H is the heavisede distrobution and δ is diracs distributin. So I tried liek this : <(H*δ)',φ>=-<H*δ,φ'>=-<δ,<H,φ'>>, <H,φ'>=∫φ'dx=φ =>...

Hi, I am trying to get the 3 dimensional convolution of a 3 dimensional function with itself using Matlab. g(x,y,z) = h1(x,y,z) 3dconvolute with h1(x,y,z) As the 3d function is symmetrical in the x,y direction(a circular function), I have reduced the function to a 2 dimensional...

Homework Statement Use the Laplace transform to solve the given initial-value problem. y'' + 9y = cos(3t), y(0)=2, y'(0)=5 Homework Equations L\left\{y''\right\} = s^{2}Y(s)-sy(0)-y'(0) L\left\{y\right\} = Y(s) L\left\{cos(kt)\right\} = \frac{s^{2}}{s^{2} + k^{2}}, s>0...

Homework Statement Sketch this function in matlab g = 3cos (10pi t) convolved with delta(t+1/10) Homework Equations The Attempt at a Solution I just need the full code to do it as an example so that I can follow up easily. thanks

Hello, I was wondering if there exists a (iso)morphism which preserves the operation of convolution, in respect to the pointwise-addition operation. For example: it is well known that the Discrete Fourier Transform is a morphism which preserves convolution in respect to...

Homework Statement I want to plot the convolution of 2 discrete funtions, for example: rect1 [n] and sin (2*pi*n/9), how can i do that? thanks! :smile: Homework Equations The Attempt at a Solution

Hello, I noticed that it is possible to define an inverse for the convolution operator so that a function f convolved by its convolution-inverse f^{\ast-1} gives the delta-function: f \ast f^{\ast-1} = \delta http://en.wikipedia.org/wiki/Convolution#Convolution_inverse Which is the family...

Homework Statement x={1,2,3,1} zero n is at 2. y={4,5,6,7,8} zero n is at 6 I´m not sure how to do it when zeros are not at the same place Can you show me the first three steps: y(0) y(1) and y(2) x(n)y(n-k)