The convolution of two functions with different parameters

1. Dec 11, 2013

S_David

Hello all,

What is the result of this (linear) convolution:

$$s(t)\star\delta(\tau-\tau_p)$$

where s(t) is a continuous signal, δ is the Dirac delta function, and \tau_p is a constant.

2. Dec 11, 2013

cpscdave

Anything convoluted with the Dirac is its self. So give that you've shifted the dirace by tau the result would be s shifted by tau as well

3. Dec 11, 2013

S_David

You mean shifted by tau_p, right? But here the Dirac is a function of tau shifted by tau_p while s(t) is a function of t!! Does this matter?

4. Dec 11, 2013

cpscdave

Hmmmm I did't notice that the dirac was using tau... I would think that is a typo in the question as it doesnt make sense. However to be fair just cause I haven't seen soemthing doesn't mean it doesnt make sense in some context...

With convolution the only time I've seen tau used as a varible is with the integral definition of the convolution operation...

Sorry I guess I should've read the question more carefully :(