Convolution Definition and 338 Threads

I have a problem/error that I believe is very simple, but I am unable to determine what the issue is nonetheless. I am trying to convolute an image with an impulse response (IE, h = [1 2 3]), but I get incessant errors and I am unsure as to why. My code is: A =...

for linear time invariant system, y(t)=h(t)*x(t) where y(t) is the output , x(t) is the input and h(t) is the impulse response.(* is the convolution) The definition of convolution is y(t)=integration from -infinity to +infinity (h(tau)x(t-tau)d(tau) p/s: i don't know how to use...

I need a help in solving this convolution. Anybody has any idea? i don't know how to integrate a function multiplied with delta function and a delay function as attached. Thank you

Homework Statement http://img166.imageshack.us/img166/1162/untitledte2.jpg Homework Equations Convolution y[n] = x[n] * h[n] The Attempt at a Solution I've never done convolutions going backwards.. right off the bat, I know I'll noly have 2 terms in the convolution sum...

Homework Statement A DT system has the unit response h[n] = (0.2(1.3)^n)u[n]. You then input x[n] = sin(n*pi/2)u[n]. Find the convolution. Homework Equations None. The Attempt at a Solution >> n = 0:30; >> h = 0.2*(1.3).^n; >> x = sin(n*pi/2); >> s = conv(h,x); I left out u[n] because we...

I know this is elementary but I'm having trouble with proofs of some of the convolution properties: 1. f * (g * h) = (f * g) * h 2. (cf) * g = c(f * g) = f * (cg) Please show me the proofs step by step or lead me to a link where the detailed proofs are displayed. Sorry for such...

I was just wondering if anybody could point me towards a good convolution tutorial, both discrete and continuous, with examples on both applied and pure mathematics (preferably, not geared towards electrical engineering). I think I have a decent grasp on it, but sometimes things just go blank...

I want to study the convolution in more details. So if you can provide me by any link to find a brief study for the convolution.

Hello. I'm studying signals and systems on my own this summer and I'm trying to get a good grasp of the convolution. I think I understand it mathematically enough to do some problems, but I don't have a firm grasp by any means. I'm studying both discrete and continuous time cases. Before I...

Homework Statement Consider a linear system with the impulse response: g(t) = 3x^2 - 4x + 7 for t>0 and 0 otherwise. Find the output for the input f(t) = t for t \geq 0 and f(t) = 0 for t<0. Homework Equations \[ \int_{-\infty}^t f(t - \tau)g(\tau)\,d\tau\] The...

I have two convolution problems, that I would like to be sure are right. If someone wouldn't mind the fun job of checking these, that would be great. QUESTION: Compute the convolution of x(t) and h(t) where: 1: x(t) = u(t) h(t) = e^{-at}u(t), \,\,\, a>0 2. x(t) = u(t) -...

Homework Statement Using convolution theorem for Laplace theorem,, show that Homework Equations inverse Laplace transform (1/(S^3/2*(s-1)) = (2*e^t)/Pi^1/2 intregral (from 0 to t) e^-x*x^1/2dx. The Attempt at a Solution The inverse Laplace above is a product of 1/s^3/2 and...

Homework Statement Right I'm having a lot of problems with convolution in general. I'll give an example of a question that I understand and why I think I understand it... and then one I don't at all. So: Consider a system with the impulse response g(t) = 0 for t<0, e^{-5t} for t \geq...

Given two independent variables with these simple density functions: f(x) = \left\lbrace \begin{array}{ll} \frac{1}{2} &\mbox{ if } 0 < x < 2 \\ 0 &\mbox{otherwise} \end{array} \right. g(y) = \left\lbrace \begin{array}{ll} \frac{1}{3} &\mbox{ if } 1 < y < 4 \\ 0 &\mbox{otherwise}...

i am asked to find f(x) s.t. exp(-xsqd/2) =1/2the integral (-inf to +inf) of exp[-|x-u|f(u)du. I have got as far as to show that the transform f(k)=(1+ksqd)exp[-ksqd/2) and my notes show that this implies the next line which is f(x)=exp[-xsqd/2] -[exp(-xsqd/2)]'' {'' denotes twice...

I just realized that the convolution of any function with itself many times will ultimately give a gaussian. I was just wondering if there was a function that was an exception to this?

The following is all in discrete time, n is an integer We are given that: h_2(n) = \delta ( n ) + \delta ( n-1 ) I want to find the convolution of h2[n]*h2[n]. I don't really understand how to solve this properly. So, y(n) = \Sigma_{k=-\infty}^{k=\infty} (\delta(n)+\delta(n-1)) \times...

I need someone to explain to me what convolution is I have textbooks that explain it, and I also can google it! lol but nothing seems to help, so I probably need a person to explain it to me in simple words.

Can someone explain convolution to me. I have read three different books and gone to office hours and am not getting the fundamentals.

Given f,g in L^1(R), I'm given the inequality: ||f * g||_1 \leq ||f||_1 ||g||_1 And now I'm supposed to derive the conditions for equality to hold. I keep going around in circles. So far, I can show equality holds iff there is some real function \phi(x) such that e^{i \phi(x+y)} f(x) g(y)...

My notes (from a physics course) justifies the following equality by invoking the convolution thm: \int_{-\infty}^{+\infty} \chi(\omega)\vec{E}_0(\omega)e^{-i\omega t}d\omega=\int_{-\infty}^{+\infty} \chi(\tau)\vec{E}_0(\tau-t)d\tau From a mathematical standpoint (i.e. without reference to...

I really need some help... this is a signal analysis course homework & it is reallly important... x(t) = sinc(x) h(t) = sinc(x) I need to solve this convolution problem in any way... i tryed solving it using MATLAB but i really need some help... thanks

anyone know how to prove that it is commutative... as if f *g = g*f

Any hints to this problem? "Assume the solution to a differential equation is given by \frac{dy(x)}{dx}+ay(x) = f(x) where y(0)=y_0 and a is a constant. Show how y(x) can be written as a convolution of f(x) and an exponential e^{ax}." The only hint we got from the prof was to multiply...

Hi, all. Just a little confused over this one (okay...a lot confused): convolution of f(x) and g(x) from -inf to inf where f(x) = e^-x and g(x) = x I would really appreciate some pointers on this one. thanks, Bailey (edit) forgot the range

I'm having trouble understanding convolution. In particular, in convolving h(t) and x(t), I have no idea what to do when x(t) = u(t-1). So for example, if h(t) = exp(-at)u(t) an x(t) = u(t-1). Is this even the right set up? I don't think it is. \int_o^t e^{-a(t-T)}u(t-1)dT the other idea I...

How do you go about convolving when x(t) = u(t-1)? Can you just make the limits of integration 1 to t instead of 0 to t?

Hi everybody. Some students have asked me about problem 2.13 in Mallat's book "A wavelet Tour of Signal Proccessing". After some work on it, I think is not completely correct. I think some hypostesis on modulus of continuity are needed. I attach the statement. Esentially, what it says...

Hello everybody, I am new in this forum and I have a problem. First of all, I am not a mathematician, I am an engineer that is using the Laplace transform. Considering this, please do not be too formal in the answers... INTRODUCTION: The LAPLACE transform of a function f(t) is...

hello Why shud one use convolution ?Inorder to get the state transition matrix from x'=Ax+Bu x(t)=exp(at)x(0) + integral[exp(a(t-tau)) bu(tau) dtau where tau is the variable of convolution. i have read that convolution is used when integration is reqd,for instance,in capacitors and...

Anyone know how to calculate the error correcting capability for a convolution code? My boss basically is giving me pressure to come up some answer by the end of this week... I won't have time to read things deep... My first question is: For a particular convolution code with a rate k/n, is...

Convolution & Inverses Given an impulse response h[n] to a system, and the impulse response g[n] of the inverse system, why is h[n] * g[n] = \delta[n]? Where the * sign is used to denote convolution.

I'm an EE student currently taking a Systems & Signals class. I've been searching high and low for information about convolution sums and convolution integrals. (Currently using the Haykin/Van Veen text). Here's my problem: I'm not grokking how the original input signal morphs into the output...

Hi. Suppose I have a function T(x,t), units are in Kelvins. I then do a convolution with a gaussian G(t), and the result is also in Kelvins. What are the units of the gaussian G(t)? Thanks.

Can anyone get me started with the following transforms using convolution theory? L^-1 {1 / (s^2+k^2)^2} and L^-1 {8 / (s^2+1)^3} Any help would be greatly appreciated CA Casanovamp@yahoo.com

How do I do this problem? C. Convolution Method " - ,c-do..U'."',,.. The convolution of two functions g andfis the function g "f defined by (g * f)(t) = J>(t - v)f(v)dv . The aim of this project is to show how convolutions can be used to obtain a particular solution to a nonhomogeneous...

hey, i did my undergrad in music and english and now am lost beyond reckoning with the impulse response stuff in my postgrad. Could anyone help with these exercises? They're examples from my lecture notes and have no idea how my lecturer got the answers. Please help? Ex.1) Show that x(t)*h(t)...

hey, i did my undergrad in music and english and now am lost beyond reckoning with the impulse response stuff in my postgrad. Could anyone help with these exercises? They're examples from my lecture notes and have no idea how my lecturer got the answers. Please help? Ex.1) Show that...