Suppose a DT signal x[n] satisfies
1. x[n] is periodic and period N=6.
2. $ \sum_{n=0}^{5}x[n]=5 $
3.$ a_{k+2} = a_k $
Find x[n].
Answer:
from 1 we have that x[n]= $ \sum_{n=0}^{5}a_k e^{-jk \frac {\pi}{3} n} $
from 2 we have $ a_0 = avg = \frac {5}{6} $
from 3 we have $ a_2 = a_4= a_0 = \frac {5}{6} $
