# Help on prooving a summation formula

## Homework Statement

I need some advice on prooving this formula (f is an arbitrary function):

$\sum^{N}_{t=1}$$\sum^{N}_{s=1}$f(t-s)=$\sum^{N-1}_{τ=-Ν+1}$(N-|τ|)f(τ)

## Answers and Replies

Ray Vickson
Homework Helper
Dearly Missed
What have you done so far? Have you tried small examples, like N = 2 or N = 3?

RGV

Well its easy to see that it works with examples like N=2 or N=3. For example for N=2 the value of both sides is f(1)+f(-1)+2f(0). Same for N=3. Im thinking that maybe I should do a variables change in the first double sums, to end up to a more common summation formula, but Im kinda stuck.

EDIT: We can consider that s and t are integers, or that the arbitrary f() function represents a discrete time signal.

Last edited:
HallsofIvy