Convolution Definition and 338 Threads

Hello. I have a problem convolving two functions. I have attached a file with the problem in details, and will be very grateful if someone can provide me with a proper explanation. Thanks! :shy:

Does anyone know how to take the partial derivative of a convolution integral where the derivative is taken with respect to one of the functions of the convolution integral? In the following example, the best I can come up with is: \frac{\partial}{\partial g(t)}\int...

Homework Statement Hi, I am wondering how to Laplace transform this expression f(t)=\int^{\tau}_{0} g(\tau)f'(t-\tau)d\tau or more precisely f(t)=\int^{\tau}_{0} sin(8\tau)f'(t-\tau)d\tau The f'(t-\tau) gets me confused. Homework Equations \int^{\tau}_{0}...

What is right definition? (f*g)(x)=\frac{1}{\sqrt{2\pi}}\int^{\infty}_{-\infty}f(x-\xi)g(\xi)d\xi or (f*g)(x)=\frac{1}{2\pi}\int^{\infty}_{-\infty}f(x-\xi)g(\xi)d\xior (f*g)(x)=\int^{\infty}_{-\infty}f(x-\xi)g(\xi)d\xi this is for me huge problem. For example f*\delta=f or f*2\pi\delta=f...

I'm struggling to find a function E(t) which is the energy inside a sphere with energy density \rho(t,r) where the radius r \equiv r(t) is itself a function of time. This E(t) = 8\pi \int_0^{r(t)} \rho(r,t) dr doesn't make sense, does it ? Is the thing I'm looking for some kind of...

Homework Statement h(t) = u(t) (the unit step function) x (t) = e-t The Attempt at a Solution There is only one interval where the two functions overlap, and that's from 0 to t. The integral from 0 to t of e-\tau d\tau = -e-t Doesn't look right to me... what am I doing wrong? EDIT: This is...

how would I show that y'(t) = x(t) * h'(t) and y'(t) = x'(t) * h(t) I know that in an LTI system y(t) = x(t) * h(t) = \int x(\tau) * h(t-\tau) from \infty to -\infty But how would I go about trying to prove the first two equations?

how would I show that y'(t) = x(t) * h'(t) and y'(t) = x'(t) * h(t) I know that in an LTI system y(t) = x(t) * h(t) = \int x(\tau) * h(t-\tau) from \infty to -\infty But how would I go about trying to prove the first two equations?

Homework Statement x(t) is input, h(t) is the impulse response, y(t) is output Find the system response to the input x(t) x(t): http://img10.imageshack.us/img10/5157/55570988.jpg h(t): http://img593.imageshack.us/img593/1079/52492104.jpg Homework Equations Now I know the...

Hi There The associative property of convolution is proved in literature for infinite interval. I want to prove the associative property of convolution for finite interval. I have explained the problem in the attached pdf file. Any help is appreciated. Regards Aman

Apparently, when convolving, for example: [δ(ω-π) - δ(ω+π)] * (δ(ω+50π)-δ(ω-50π)) the result is δ(ω+49π)-δ(ω-51π)-δ(ω+51π)+δ(ω-49π) where δ() is the Dirac delta function, * the convolution operator and ω the frequency variable How do we get to this? Can you help me on the intuition in...

Homework Statement Hello, I'm revising this summer for signals and systems and I came across this convolution cos(t)*u(t) Homework Equations having two signals x(t) and h(t), where x(t) is the input signal and h(t) the impulse response the output y(t) is given by y(t) = x(t)*h(t) =...

hey guys, i hope you can help. my task is to analyse data of raman spectroscopy. therefor i have to deconvolute it. that means the data must have been convoluted somewhere. is it true that the raw data which i receive is convoluted already? or is it common to convolute the data "active"...

Hi there. We know that Convolve[f,g,x,y] = f[y] if g = diracdelta. My question is, what should be g so that Convolve[f,g,x,y] = f[y1] where y1 is a parameter of the g function. I.e. Is there any function g such that, when convolved with another f, gives the evaluation of f on a given point?

I fail to understand a step made in this proof: http://en.wikipedia.org/wiki/Convolution_theorem" more specifically the last step where the integral is written as a product of 2 separate integrals (each equal to a Fourier transform): from: to: I'm quite rusty on my integration, but as far I...

finding the FT of x(t)=sin(πt) sin(50πt) : ( '*' is the convolution operator) its FT X(Ω)=(1/2π) F(sin(πt)) * F(sin(50πt)) = (1/2π) jπ(δ(Ω+π)-δ(Ω-π)) * (jπ (δ(Ω+π)-δ(Ω-π)) ) (a) from my professor's solution it next goes: = (π/2) (-δ(Ω+π)+δ(Ω-π)) * ((-δ(Ω+π)+δ(Ω-π)) )...

Hi there. I must calculate the convolution between these functions f(t)= e^{-t} H(t) g(t)=e^t H(t) H(t) the unit step Heaviside function. So I have to find: f \star g This is what I did: f \star...

Homework Statement Consider the signal x(t)=cos(4t)+cos(5t)+cos(6t), and the SLIT with impulse response: h(t)=\begin{cases} 1, & \mbox{if } |t|<T \\ 0, & \mbox{if } |t|>T \end{cases} For what value of T is the output of the system y(t) equal to Acos(4t)+Bcos(5t), when x(t) is the...

it might sound a bit hilarious.. some where i read about image processing where on the original image some operations were done (dealing with something related to convolution may be ) and say image A was obtained.. again another set of operations ( dealing with Fourier transform on the image...

Homework Statement Convolve an arbitary function f(t) with comb(t) [a sum of delta functions that run from -infinity to infinity with spikes at t = nT]. Is the convolution an array of copies of f(t) or is it a set of discrete points such that f(t) is returned at every t = nT? Homework...

Homework Statement δ = dirac delta x[n] = δ[n] + 2δ[n-1] - δ[n-3] h[n] = 2δ[n+1] + 2δ[n-1] y[n] = x[n]*h[n] Homework Equations y[n] = x[n]h[n] = \sumh[k]x[n-k] The Attempt at a Solution I have graphed the x[-k] and h[n], the solution saids y[n] = h[-1]*x[n+1] +...

I am trying to understand wikipedia's definition of convolution: http://en.wikipedia.org/wiki/Convolution#Definition . I'm wondering why g(tau) is flipped in the definition.

Hello everyone, please help me to answer this question. Is this true that any LTI system can be characterized by either its impulse response or engenvalue?

Hi all, I am now doing revision for one of the statistics module. I am having some difficulty to proove the following: Given n iid Exponential distribution with rate parameter \mu, using convolution to show that the sum of them is Erlang distribution with density f(x) = \mu...

As a double major in physics an electrical engineering, I noticed that graphical convolution is used in both signal processing and quantum mechanics. In my signals course I couldn't help but notice that sometimes the professor would just convolved the function from straight integration, and...

The problem: Solve the integral equation \int\stackrel{\infty}{-\infty}exp(-abs(x-y))u(y)dy+u=f(x) for -\infty<x<\infty. The solutions say "Use the convolution theorem to find u(x)=f(x)-\frac{4}{3}\intf(t)exp(-3abs(x-t))dt." The Convolution Theorem in my book states "If the functions f(x)...

hi, i have trouble in understanding the concepts of the impulse response first of all, let's assume that we have a signal y[n] = x[n] which is time invariant and linear, hence if I understand correctly linear means that if for input a*x1[n] we have an output a*y1[n] b*x2[n] we...

Homework Statement The signal x(t) = u(t-1) - u(t-3) is the input to an LTI system with the impulse response h(t) = u(t-5) - u(t-8). the system is initially at rest. a) Compute the output y(t) of this system using convolution. b) Compute the output y(t) of this system using the Laplace...

Homework Statement i have this graph http://img858.imageshack.us/img858/1346/56954457.png and i need to find h-1[k] i don't understand, i know that the impulse response is the response for input -> δ[n], in this case it will be δ[n+1], but i don't understand how to calulate the response...

Homework Statement Calculate f*f where f is the indicator function (-1,1) Homework Equations The convolution f*g of functions f and g is defined by: f*g(x)=\int^{\infty}_{-\infty} f(x-y)g(y)\ dy The Attempt at a Solution I haven't really done convolution before as I am teaching myself, so...

Hi, I have encountered with this: \delta[y-a]*\delta[y-b] where a and b are positive real numbers, and * denotes convolution. How to do this in both continuous and discrete cases? In Wikipedia, they say that: \int_{-\infty}^{\infty}\delta(\zeta-x)\delta(x-\eta)\,dx=\delta(\zeta-\eta) Can I...

Hi - I'm trying to work out the following convolution problem: I have the following integral: \int^{\infty}_{-\infty}p(x)U(x)e^{-i \omega x}dx Where p(x) is any real function which is always positive and U(x) is the step function Obviously this can easily be solved using the...

Please help me to solve these problems in my homework. I should deliver it tomorrow.

for... p'_n = {1 Union Prime Numbers} M_n = n-th Mersenne Number (2^n - 1) T_n = n-th Triangular Number (n^2 + n)/2 x = {0,1,2,3,13} --> F_(0, 1/2, 3, 4, 7) for F_n = n-th Fibonacci Number Then... ((p'_x*p'_2x)*(M_x - (T_x - 1))) / ((T_(M_x) - T_(T_x - 1)) is in N EXPANSION ((1*1)*(0 +...

Im struggling to find proof for this suspicion I have; Given is a function f(t) and a normalised function h(t), and their convolution; f(t) * h(t) = g(t) Is it true that \int fdt = \int gdt ?

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...

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 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...

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...

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...