Convolution Definition and 364 Threads

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    How Can I Solve a Density Function Using the Fundamental Theorem of Calculus?

    hi, i'm given the density function fx(t) = 0 (t<0) fx(t) = 2t (0<t<1) fx(t) = 0 (t>1) how can i solve this using the fundamental theorem of calculus? i had a similar situation before where my function was: fx(t) = 0 (t<0) fx(t) = 1 (0<t<1) fx(t) = 0 (t>1) and the g(t) i came to...
  2. S

    Understanding Convolution: h(t) & x(t) w/ x(t)=u(t-1)

    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...
  3. S

    Convolution with time shifted step function.

    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?
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    Convolution with a sinc gives uniform approximation to a function

    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...
  5. T

    Convolution integrals with Dirac's delta and its derivatives

    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...
  6. N

    Why should one use convolution ?

    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...
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    Convolution Code and Error Correcting Capability

    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...
  8. L

    Convolution - Can someone explain this solution?

    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.
  9. B

    Convolution Sums: Understanding the Input & Output Signals

    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...
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    Convolution with a gaussian G(t)

    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.
  11. N

    How Does Convolution Theory Apply to Inverse Laplace Transforms?

    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
  12. A

    Solve Convolution Method Problems Easily

    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...
  13. L

    Impulse response and convolution? any help from anyone?

    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)...
  14. L

    Help with impulse response and convolution?

    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...
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