Convolution Integral Properties


by benfrankballi
Tags: convolution, integral, properties
benfrankballi
benfrankballi is offline
#1
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 Phys.org
Better thermal-imaging lens from waste sulfur
Hackathon team's GoogolPlex gives Siri extra powers
Bright points in Sun's atmosphere mark patterns deep in its interior
jackmell
jackmell is offline
#2
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