Convolution Definition and 364 Threads

SORRY, I figured it was wrong of me to hijack someone elses thread with my query so I will start my own thread, my apologizes in advance for I will also post a thread within the Math forum... I am new here and I bring a similar question for my first post... I want to know how to do a...

Hi everybody, I have question: Why can you do Convolution filter in the frequency Domain ? I mean, when you apply a filter to an image in the spatial domain, it 's easy. You've got for example your sobel 3x3 kernel that you apply on every pixel of your image. Easy. But when you convert...

Hi everyone, I need help finding the Fourier transform of Cos(10t)sin(t) i know that i need to find the transform of cos and sin and then convolve them, but i m not sure how to convolve delta function. I would really appreciate any helps.

Homework Statement Prove the associativity law and the distributive law for convolution: (1) prove F*(G+H)=(F*G)+(F*H) (2) prove: F*(G*H)=(F*G)*H Homework Equations The Attempt at a Solution (1) proof: using the definition of the laplace using convolution Left hand side...

Homework Statement using the Fourier Transform convolution theorem should be true that i^{m+n}D^{m}\delta (u)D^{n}\delta (u)= A \mathcal F _{u}(\int_{-\infty}^{\infty}dt (t-x)^{m}t^{n} ) Homework Equations - Fourier transform convolution theorem (would be valid for...

Homework Statement trying to determine a general method for doing inverse-Laplace transforms of a product of two Laplace Transform (L.T.) functions f1(s) and f2(s) where f1(s) and f2(s) are the LTs of F1(t) and F2(t). The scenario is for calculating the convolution integral for F1(t)*F2(t)...

OK. I understand almost everything I need to know in order to do a convolution problem except how to set up what needs to be integrated. The way my professor does it is: 1) flip the impuse 2) move h(t) over x(t) - we usually do this in 5 different regions 3) for each region the bounds have...

Hi, I am a Physics PhD student and am trying to understand the Convolution theory. My original background is Chemistry so I am finding the maths very difficult. I work in condensed matter and want to generate a c++ code that will convolute some theoretical data I generate with a Gaussian...

I having a hard time understanding an aspect of the definition of the convolution of two functions. Here is the lead up to its definition... It goes on to discuss what the observed distribution h(z) will be if we try to measure f(x) with an apparatus with resolution function g(y). And tries...

Hey guys, I'm having trouble doing ct convolution i'm trying to convolve two signals together ie, the input x(t) and the impulse response h(t). basically, knowing the impulse response of an LTI system, you can find out the response y(t) to any arbitrary input x(t) using the convolution...

Hi, there! That's probably the most relevant forum thread where I can consult pros about my problem. Well, I'm a visual programmer and quite far of Spectra Physics to what my issue's dramatically related to. Specifically, I need to implement in C# the frequency-domain signal filtration (with a...

I've read on a bunch of websites that the convolution of two gaussians produces another gaussian however I have not seen this integration worked out. I am working on an integral which has a similar form as this convolution so it would be a great help too see. Does anyone know a book or website...

given a function f(t) could we define the operation f*f*f*f*f*f*f*f**f*f*f*f*...*f n times ? here the operation '*' means convolution of a function if n=2 i know the expression (f*f)= \int_{0}^{x}dt f(t)f(t-x) but i would like to see if this can be applied to arbitrary order ...

Homework Statement Find R(\tau) if a) S(\omega) = \frac{1}{(4+\omega^2)^2} Homework Equations I have given \frac{4}{4+\omega^2} <==> e^{-2|\tau|} The Attempt at a Solution So S(\omega) = \frac{1}{(4+\omega^2)^2}= \frac{1}{16}\frac{4}{(4+\omega^2)}\frac{4}{(4+\omega^2)} R(\tau)=...

How do you do the convolution of exp (x(n))*u(x(n)) and exp(x(n-1))*u(x(n-1)) where u(x) is the unit step function. Thanks.

Alright...so I've got a question about the convolution of a dirac delta function (or unit step). So, I know what my final answer is supposed to be but I cannot understand how to solve the last portion of it which involves the convolution of a dirac/unit step function. It looks like this: 10 *...

Let X,Y~U(0,1) independent (which means that they are distributed uniformly on [0,1]). find the distribution of U=X-Y. well intuitively U~U(-1,1), but how to calculate it using convolution. I mean the densities are f_Z(z)=1 for z in [-1,0] where Z=-Y and f_X(x)=1 for x in [0,1], now i want to...

For the question stated in the pictures attached to this message, for part d of the question, I just can't picture why the convolution of the two signals is 1. Can someone please explain how this would be the case as the triangular signal is sweeping through all the delta functions? Thanks.

Homework Statement f(t) = e^{-m't}u(t)}, h(t) = e^{-mt}u(t) f(t)*h(t) Applying l'hopital's to find the result in the limit m' \rightarrow m Homework Equations lim_{t\rightarrow c}\frac{f(t)}{h(t)} = lim_{t\rightarrow c}\frac{f'(t)}{h'(t)} The Attempt at a Solution h(t -...

Homework Statement Compute the following y(t)=e^{-3t}u(t)\ast u(t+3) Homework Equations u(t) is the unit step function. The Attempt at a Solution I get confused with these for some reason... y(t)= \int^{+\infty}_{-\infty}e^{-3 \tau}u(\tau)u(t-\tau+3)d\tau This is where...

Homework Statement It is a theorem in my book that if f and g are two Lebesgue integrable complex valued functions on R, then the integral \int_{-\infty}^{+\infty}|f(x-y)g(y)|dy is finite for almost all x in R. Why not all? f is integrable, hence bounded, say, by M. Therefor, whatever x, we...

Dear Member, i need to know some details on convolution... For e.g., I have X values from 1 to 186 and the corresponding Y values. If i plot i will get some spectra...Now i want to convolute that spectra/XY values with a Gaussian function with FWHM of 1.2 meV. Do you think is it possible to do...

My textbook provides a proof but there's one thing about the proof i do not understand it starts assuming L{f(t)} = the laplace integral with the f(t) changed to f(a) same goes with L{g(t)} as it changes it to g(b) i understand the big picture>>starting from a product of 2 L transforms...

Homework Statement Hi, I'm having some problem with one of my final exam study questions, and I'm hoping someone can help me out a little. here is the problem: Let Y_{1},Y_{2},...,Y_{n} denote random samples of numbers from a uniform distribution on the interval [0,1]. Denote the...

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...

Hello, I am trying to examine the following differential equation: diff(M(a), a) = Lambda * ( 1 - epsilon * int(M(b)*exp(-sigma*(a-b)), b = 0 .. a) ) - mu * M(a) I found out that this kind of equation can be solved for M(a) by applying Laplace-Transformation, solving for...

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