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: Discrete Time Convolution of Sums

  1. Mar 27, 2013 #1
    Evaluate the following discrete-time convolution:

    y[n] = cos([itex]\frac{1}{2}[/itex][itex]\pi[/itex]n)*2[itex]^{n}[/itex]u[-n+2]

    Here is my sloppy attempt:

    y[n] = [itex]\sum[/itex]cos([itex]\frac{1}{2}[/itex][itex]\pi[/itex]k)2[itex]^{n-k}[/itex]u[-n-k+2] from k = -∞ to ∞

    = [itex]\sum[/itex]cos([itex]\frac{1}{2}[/itex][itex]\pi[/itex]k)2[itex]^{n-k}[/itex] from k = -∞ to 2

    We can re-write the cos as [e[itex]^{0.5j\pi}[/itex]-e[itex]^{-0.5j\pi}[/itex]]0.5

    using the property of summation of geometric series:

    0.5[itex]\sum[/itex]2[itex]^{n-k}[/itex](e[itex]^{0.5j\pi k}[/itex]-e[itex]^{-0.5j \pi k}[/itex])

    from k = -∞ to 2

    so more or less am I on the right track?
  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