EEE 321 Signals and Systems Midterm

EEE 321 Signals and Systems Midterm
June 25, 2016
120 Minutes


Name :
Number:



Q1 6 + 6 + 6 + 6 (24 pts)
Q2 10 + 12 (22 pts)
Q3 10 + 10 + 10 (20 + 10 pts)
Q4 8 + 4 (12 pts)
Q5 10 + 12 (22 pts)
TOTAL (100 + 10 pts)


Instructions No books or notes are al-
lowed. No Access to Internet. For full
credit provide complete details of your work!

, Q1: For each of the following continuous- or discrete-time sys-
tems, determine whether the system is (i) linear, (ii) time invariant,
(iii) causal and (iv) stable.

a) (6 pts) y(t) = x(t − 3) − x(3 − t)
b) (6 pts) y(t) = sin(2t).x(t − 1)
c) (6 pts) y[n] = x[n].x[n + 2]
d) (6 pts) y[n] = 2x[n] − 3n


Q1 Answer:
a)
y1 (t) = x1 (t − 3) − x1 (3 − t), y2 (t) = x2 (t − 3) − x2 (3 − t)
x(t) = ax1 (t) + bx2 (t) → y(t) = x(t − 3) − x(3 − t)
y(t) = ax1 (t − 3) + bx2 (t − 3) − ax1 (3 − t) − bx2 (3 − t)
y(t) = a(x1 (t − 3) − x1 (3 − t)) + b(x2 (t − 3) − x2 (3 − t)) = ay1 (t) + by2 (t)
LINEAR


x1 (t) = x(t − t0 ) → y1 (t) = x1 (t − 3) − x1 (3 − t)
y1 (t) = x(t − t0 − 3) − x(3 − t − t0 ) 6= y(t − t0 )
TIME VARYING

For t < 0, y(t) depends on future values of x(t), this system is
NOT CAUSAL

If |x(t)| < B, ∀t,

|y(t)| = |x(t − 3) − x(3 − t)| ≤ |x(t − 3)| + |x(3 − t)| < 2B ∀t
STABLE




1