Guess the Periodic Signal
Find a DT signal that satisfies these properties:
1. period N=2
2. $ \sum_{n=0}^3 x[n] = 2 $
3. $ a_1=3 \! $
Solution
1. a period of 2 gives us
$ x[n] = \frac{1}{2}\sum_0^{N-1} a_ke^{jk\pi n} $
2. $ a_0 = 1 \! $
3. $ a_1 = 3 \! $
Giving us:
$ x[n] = 1 + 3e^{j\pi n} \! $
