I need a simple solution on how to prove this so that i can solve a convolution problem:

where m is a positive integer

thank you and your help is appreciated

Printable View

- January 15th 2011, 12:47 PMTechnicianEngineerhow do i prove this summation?
I need a simple solution on how to prove this so that i can solve a convolution problem:

where m is a positive integer

thank you and your help is appreciated - January 15th 2011, 02:57 PMAckbeet
Assuming your is the Kronecker delta, and not the Dirac delta, the proof is actually quite straight-forward, and follows from the definition of the Kronecker delta, which is as follows:

So your delta function is 1 when what happens? What implications does that have for your summation? - January 15th 2011, 04:07 PMTechnicianEngineer
thank you for replying to my thread

the given is a convolution of a discrete signal which is shown in the equation below

i need to find how it equates to x(n-m) and i quite need the solution for it.

i am newb in summation and forgot about how to do it

and yes that is the**delta dirac**symbol not the Kronecker delta

your help is appreciated - January 15th 2011, 04:28 PMAckbeet
Oops, I think I didn't define the Kronecker delta correctly. I think what I defined actually

*was*the discrete Dirac delta. The Dirac delta, in this case, "picks out" one term in a sum (this is actually how the continuous version of the Dirac delta distribution is defined: with an integral). So, you have the following:

So the delta in your sum is 1 only when and zero elsewhere, which means that every single term in your sum is zero except for the one when Do you see where this is going?