Repeat Prob XXXXXXXXXXfor the exponentials Prob. 4.2-6 The following signals are in the form e λn . Express them in the form γ n . (a) e −0.5n (b) e 0.5n (c) e −jπn (d) e jπn In each case, show the...

Prob. 4.2-6

The following signals are in the form e^λn. Express them in the form γⁿ.

(a) e^−0.5n

(b) e^0.5n

(c) e^−jπn

(d) e^jπn

In each case, show the locations of λ and γ in the complex plane. Verify that the exponential is growing if γ lies outside the unit circle (λ in the RHP), is decaying if γ lies within the unit circle (λ in the LHP), and has a constant envelope if γ lies on the unit circle (λ on the imaginary axis).