1. Limited time only! Sign up for a free 30min personal 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!

Homework Help: Signal Windowing Help

  1. Nov 6, 2011 #1
    1. The problem statement, all variables and given/known data

    [itex]p[n]=x[n]w[n][/itex], where [itex]w[n][/itex] is the rectangular window.

    [itex]x[n]=\sum_{k=-∞}^{∞} δ[n-k][/itex]

    [itex]w[n]= 1,[/itex] for [itex]-M≤n≤M;[/itex]
    [itex] = 0[/itex] otherwise​

    1. What is [itex]X(e^{jw})[/itex]?
    2. What is [itex]P(e^{jw})[/itex] when...

    [itex]j[/itex] is the imaginary number. (it's the same as [itex]i[/itex].)

    2. Relevant equations

    3. The attempt at a solution

    [itex]X(e^{jw})=2\pi\sum_{k=-∞}^{∞}δ[n-2\pi k][/itex]

    I found [itex]X(e^{jw}[/itex] fairly easily, but I can't find [itex]P(e^{jw})[/itex] for either case of M. The answers from the book are below. Can someone tell me how I solve for this? I don't see why [itex]X(e^{jw})[/itex] is so different from [itex]P(e^{jw})[/itex]

    [itex]P(e^{jw})=e^{jw}+1+e^{-jw}=1+2cos(\omega)[/itex] when M=1
    [itex]P(e^{jw})=\frac{sin(21 \omega/2}{\omega/2}[/itex] when M=1
  2. jcsd
Share this great discussion with others via Reddit, Google+, Twitter, or Facebook

Can you offer guidance or do you also need help?
Draft saved Draft deleted