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).