Question 9.8: Determine if a discrete-time exponential x[n] = 2 (0.5)^n, n......

The energy is given by

\varepsilon_{x}=\sum_{n=0}^{\infty}4(0.5)^{2n}=4\sum_{n=0}^{\infty}(0.25)^{n}={\frac{4}{1-0.25}}={\frac{16}{3}}

thus x[n] is a finite-energy signal. Just as with continuous-time signals, a finite-energy signal is a finite power (actually zero power) signal. Indeed,

P_{x}=\operatorname*{lim}_{N\to\infty}{\frac{1}{2N+1}}\varepsilon_{x}=0.