Question

1. Express the following signals in the formy, plot the locations of Andy in the complex plane and indicate each signal's stability (whether the signal grows, shrinks or remains constant as k progresses)

Answer 1

→ a) Given each signal to represent as F[k] = e = y* (t=e^] e-0.5% => 1 = -0.5 - (805)* »> t = -0.52 0.006s d-plane ↑ Im (a) I-plane ↑ Im (3) os Rel) 0.6065 Rela) 1. AS Hkl a s k so the signal is stable as koo → signal shrinks with k e 0.5K -0-5 (29.5)k >> 100.5 1.6487 s-plane 13mL) & plane 1 ) u tors > Rela) Blu - 1.6683 Rel) 0.5 As 111>1 as kso the signal is unstable signal group as k increases. IT e are - a plane 7- Plane Im (1) Rel) -> Rel)

As N =1 as k progresses the signal magnitude remains constant, but alternates. d) . estk x = in (eink » f = eit = -1 y-plane n im ↑ Im LA) - Rec) -> Recy) signal magnitude As 111=1 as k progresses the remains constant, but alternates e) e ti+j)k ads 41+31) Jetet iryga o te e-(i+19), et 0.361 € JT dplane = 0.367(-1) + jo ņ Imcol - Rela) ()ع دة 1 As iki as k>O and progresses, the signal shrinks hente stable. Here stability is concluded, based on boundedness ( signal to be bound by finite value at any instant of time)