- #1

- 3

- 0

## 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

- Thread starter nrgyyy
- Start date

- #1

- 3

- 0

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

Science Advisor

Homework Helper

Dearly Missed

- 10,706

- 1,728

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

RGV

RGV

- #3

- 3

- 0

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

Science Advisor

Homework Helper

- 41,833

- 962

- #5

- 3

- 0

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

- Last Post

- Replies
- 1

- Views
- 1K

- Last Post

- Replies
- 4

- Views
- 627

- Last Post

- Replies
- 1

- Views
- 2K

- Replies
- 8

- Views
- 1K

- Replies
- 6

- Views
- 265

- Replies
- 3

- Views
- 826

- Last Post

- Replies
- 9

- Views
- 2K

- Last Post

- Replies
- 8

- Views
- 982

- Last Post

- Replies
- 1

- Views
- 1K

- Last Post

- Replies
- 2

- Views
- 2K