Help on prooving a summation formula

  • Thread starter nrgyyy
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  • #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
 

Answers and Replies

  • #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
 
  • #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.
 
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  • #4
HallsofIvy
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Looks to me like there is a change of index at work there. Since the left side of the equation involves f(t- s) and the other side f(τ), you should immediately think of τ= t- s.
 
  • #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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