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: Impulse response of recursive DT system

  1. Sep 7, 2010 #1
    1. The problem statement, all variables and given/known data

    [tex]y[n] - 1.8\cos (\frac{\pi }{{16}})y[n - 1] + 0.81y[n - 2] = x[n] + 0.5x[n - 1][/tex]
    Determine the impulse response [tex]h[n][/tex] by calculating the zero-state response with [tex]x[n] = \delta [n][/tex]

    2. Relevant equations

    [tex]y[n] - 1.8\cos (\frac{\pi }{{16}})y[n - 1] + 0.81y[n - 2] = x[n] + 0.5x[n - 1][/tex]

    3. The attempt at a solution

    [tex]y[n] - 1.8\cos (\frac{\pi }{{16}})y[n - 1] + 0.81y[n - 2] = x[n] + 0.5x[n - 1][/tex]
    [tex]y[n] = 1.8\cos (\frac{\pi }{{16}})y[n - 1] - 0.81y[n - 2] + x[n] + 0.5x[n - 1][/tex]
    [tex]h[n] = 1.8\cos (\frac{\pi }{{16}})y[n - 1] - 0.81y[n - 2] + \delta [n] + 0.5\delta [n - 1][/tex]
    The zero-state response means
    [tex]\begin{array}{l}
    y[- 1] = 0 \\
    y[- 2] = 0 \\
    \end{array}[/tex]
    So my question is how can I write out the impulse response explicitly in one expression. I think I could calculate it by [tex]h[0],h[1],h[2].....[/tex] but I want to write it out as just one expression but the recursive terms[tex]y[n - 1][/tex] and [tex]y[n - 2][/tex] are kind of throwing me off.
     
  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