Convolution Definition and 338 Threads

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 [SIZE="5"]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,[SIZE="3"][SIZE="5"] 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...

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)

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 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...

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 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...