The following problems relate to periodicity and power of discrete-time signals.

(a) Is the signal x[n] = e^j(n−8)/8 periodic? if so determine its fundamental period N₀. What if x₁[n] = e^{j((n−8)π/8)} (notice the difference with x[n]) would this new signal be periodic? if so what would the fundamental period N₁be?

(b) Given the discrete-time signal x[n] = cos (πn/5) + sin (πn/10), −∞ < n < ∞.

i. Is x[n] periodic? If so determine its fundamental frequency ω₀.

ii. Is the power of x[n] the sum of the powers of x₁[n] = cos (πn/5) and x₂[n] = sin (πn/10) defined for − ∞ < n < ∞? If so, show it.