Convolution with an delta function

[spaghetti3451]

Homework Statement

Convolve an arbitary function f(t) with comb(t) [a sum of delta functions that run from -infinity to infinity with spikes at t = nT]. Is the convolution an array of copies of f(t) or is it a set of discrete points such that f(t) is returned at every t = nT?

Homework Equations

The Attempt at a Solution

The solution depends on the domain of f(t).

 

[tedbradly]

$$f(t)*\delta(t-t_0) = \int\limits_{-\infty}^{\infty} \delta(\tau-t_0) f(t-\tau) \,d\tau=f(t-t_0)$$
via sampling property of the impulse

 

[spaghetti3451]

So what's the answer?

 

[berkeman]

So what's the answer?

That is what *you* are required to figure out.