Register to reply

Convolution Integral Properties

by benfrankballi
Tags: convolution, integral, properties
Share this thread:
Sep30-11, 09:55 PM
P: 2
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) = [itex]\int[/itex] x([itex]\tau[/itex]) * h(t-[itex]\tau[/itex]) from [itex]\infty[/itex] to -[itex]\infty[/itex]

But how would I go about trying to prove the first two equations?
Phys.Org News Partner Science news on
Hoverbike drone project for air transport takes off
Earlier Stone Age artifacts found in Northern Cape of South Africa
Study reveals new characteristics of complex oxide surfaces
Oct1-11, 05:35 PM
P: 1,666
Why not just differentiate the convolution integral:

[tex]\frac{d}{dt}\int_{-\infty}^{\infty} x(\tau) h(t-\tau)d\tau=\int_{-\infty}^{\infty} x(\tau)h'(t-\tau)d\tau=x(t)*h'(t)[/tex]

Register to reply

Related Discussions
Convolution Integral properties Electrical Engineering 1
Convolution Integral Calculus & Beyond Homework 1
Convolution integral question.. Calculus & Beyond Homework 2
Laplace convolution properties Calculus & Beyond Homework 0
Convolution integral Calculus & Beyond Homework 3