summation formulas

Discussion in 'Math' started by jut, Sep 19, 2009.

  1. jut

    Thread Starter Senior Member

    Aug 25, 2007
    224
    2
    This problem is in the context of discrete systems and signals.

    My goal is to find an equation for y(n) without the summation.

    y(n)=\sum_k k(n-k)u(k-4)u(k+2-n)

    where u(k) is the unit step function, k is from -inf to inf, and n=0,1,2,3...

    So I need to eliminate the unit step functions from the equation by changing the limits of summation:

    if k-4\geq 0 then u(k-4)=1. And so it's eliminated from my summation above.
    if k+2-n\geq 0 then u(k+2-n)=1. And it's also eliminated.

    So my limits of summation are k\geq 4 and k\geq n-2. But the limits don't define a finite range! Can anyone help?
     
    Last edited: Sep 20, 2009
  2. someonesdad

    Senior Member

    Jul 7, 2009
    1,585
    141
    You don't say whether the summation over k is over a finite or infinite range nor what the domain of n is. If it is infinite, the series clearly diverges -- you can ignore the step functions for large enough k and you're then summing terms of the form nk - k^2.

    If you remember the step function isn't unity until the argument is >= 0, then you can see the only relevant terms will be whichever of k >= 4 or k >= n+2 is larger; the smaller terms will be zero because the step function is "switched off". Then you should be able to write down closed form expressions because nƩk and Ʃk^2 are easy to find in a handbook.

    BTW, it's k >= n - 2.
     
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