1. Not finding help here? Sign up for a free 30min tutor trial with Chegg Tutors
    Dismiss Notice
Dismiss Notice
Join Physics Forums Today!
The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

Help with this Summation?

  1. Dec 15, 2011 #1
    It's been a while since I took Calc 2 and I am in a Linear Systems and Signals class right now. I'm looking at a solution on how to obtain a zero state response of a discrete time signal, but performing the summation confuses me. Can someone explain the steps they did?

    This is part A

    http://imageshack.us/photo/my-images/684/partal.jpg/

    This is part B

    http://imageshack.us/photo/my-images/11/part2sy.jpg/

    In Part A, where did the +1 come from?
    Also, how would you simplify the first fraction appearing after the equal sign of Ystep?

    In Part B, where did the -1 's come from? Originally, h[m] was just (6/5)[itex]\sum[/itex](-1/2)m + (24/5)Ʃ(1/3)m

    I have a Final next week on this stuff so, any help would be appreciated.
     
    Last edited: Dec 15, 2011
  2. jcsd
  3. Dec 15, 2011 #2

    SammyS

    User Avatar
    Staff Emeritus
    Science Advisor
    Homework Helper
    Gold Member

    Part A: Where did the 1 come from?
    [itex]\displaystyle \sum_{m=0}^{k}(-2)^m=(-2)^0+\sum_{m=1}^{k}(-2)^m[/itex]

    and of course, (-2)0=1​

    As for simplifying the fraction, they have done it quite well.
    [itex]\displaystyle \frac{1-(-2)^{k+1}}{1-(-2)}=\frac{1-(-2)(-2)^{k}}{3}[/itex]

    [itex]\displaystyle =\frac{1}{3}+\frac{2}{3}(-2)^{k}[/itex]​
     
  4. Dec 15, 2011 #3

    SammyS

    User Avatar
    Staff Emeritus
    Science Advisor
    Homework Helper
    Gold Member

    I assume the sum in the original form of h[m] started with m=1. The -1s come from the fact that in Part B, the sums start with m=0.

    BTW: You appear to still be very rusty regarding working with summations, considering that your final is next week.

    Good Luck !
     
  5. Dec 16, 2011 #4
    For Part A, the index for the final answer is m = 0 though. You have it at m=1 for (-2)m
     
  6. Dec 16, 2011 #5

    SammyS

    User Avatar
    Staff Emeritus
    Science Advisor
    Homework Helper
    Gold Member

    Yes. I left it for you to identify what is what & for you to do a little algebra.

    [itex]\displaystyle \underbrace{\sum_{m=0}^{k}(-2)^m}_{\text{from 2nd line}}=(-2)^0+\underbrace{\sum_{m=1}^{k}(-2)^m)}_{\text{from 1st line}}[/itex]
     
Know someone interested in this topic? Share this thread via Reddit, Google+, Twitter, or Facebook




Similar Discussions: Help with this Summation?
  1. Help with summation (Replies: 10)

  2. Summation help (Replies: 2)

  3. Help with summation (Replies: 4)

Loading...