Convolution in Discrete time of a function with Impulse with delay?

[Kdar]

Here is convolution:

c[k]= (0.5)^k * delta(k-1)

What do I do about delta(k-1)?
I know if it is c[k]= (0.5)^k * delta(k), then it just equal (0.5)^k

But what do I do with delta(k-1)?

 

[tiny-tim]

Welcome to PF!

Hi Kdar! Welcome to PF!

(have a delta: δ and try using the X² tag just above the Reply box )

One method is to substitute u = k - 1, solve it, then substitute back again.

 

[elibj123]

Why not start from the definition then go with it?