- #1

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## Homework Statement

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

[itex]\sum^{N}_{t=1}[/itex][itex]\sum^{N}_{s=1}[/itex]f(t-s)=[itex]\sum^{N-1}_{τ=-Ν+1}[/itex](N-|τ|)f(τ)

Thanks in advance

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- Thread starter nrgyyy
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- #1

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

[itex]\sum^{N}_{t=1}[/itex][itex]\sum^{N}_{s=1}[/itex]f(t-s)=[itex]\sum^{N-1}_{τ=-Ν+1}[/itex](N-|τ|)f(τ)

Thanks in advance

- #2

Ray Vickson

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What have you done so far? Have you tried small examples, like N = 2 or N = 3?

RGV

RGV

- #3

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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.

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

Last edited:

- #4

HallsofIvy

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- #5

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could you please help on how the limits of the left side sums would be in that case (τ=t-s)?

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