Discrete Time Convolution of Sums

1. Mar 27, 2013

Mr.Tibbs

Evaluate the following discrete-time convolution:

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

Here is my sloppy attempt:

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

= $\sum$cos($\frac{1}{2}$$\pi$k)2$^{n-k}$ from k = -∞ to 2

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

using the property of summation of geometric series:

0.5$\sum$2$^{n-k}$(e$^{0.5j\pi k}$-e$^{-0.5j \pi k}$)

from k = -∞ to 2

so more or less am I on the right track?