The convolution of a function with an impulse function delayed

the-convolution-of-a-function-with-an-impulse-function-delayed

The convolution of a function with an impulse function delayed to an instant 3 in time results in ____________

A. An advance in the function by 3 units in time

B. The function itself

C. A delay in the function by 3 units in time

D. Cannot be determined

I got this question in final exam.

My question is taken from Convolution topic in portion Digital Signal Processing of MATLAB

The correct choice is C. A delay in the function by 3 units in time

To explain I would say: The convolution of an impulse function with a function results in the function itself. But if the impulse function is delayed, the output will also get delayed by an equal amount. This is because

∫^∞-∞ f(k).δ(t-m-k)dk=f(t-m).