The convolution of two functions with different parameters

[EngWiPy]

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.

Thanks in advance

 

[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

 

[EngWiPy]

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

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?

 

[cpscdave]

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