summation formulas

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

  1. jut

    Thread Starter Senior Member

    Aug 25, 2007
    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
    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.