Home w work #1 Signal and
System Analysis
Name: ----=-----'-------L-------Open book, open notes, no calculator. Be neat, write legibly. For full credit you must show all work and justify each answer.
You may write on the both sides of the paper, and use additional sheets of paper if needed.
I. (30 %) Consider the following signal:
X ()
t
. (21r(t-T))
= 3S!Il
Determine the values ofT for which the resulting signal is:
(a) an even function oft.
(b) an odd function oft.
5
2. (30 %) Consider the signal f (t) shown below.
(a) Write an equation that describes this signal using ramp
and rect functions only.
(b) Take the derivative of the equation you found in part (a).
(c) Sketch the derivative of this signal.
/(l)
3. (40 % ) Determine if the following systems are linear, time-invariant, causal, stable, memoryless, and/or invertible.
(a) y[n] = x[n]u[x[n]]
d
(b) y(t) = d x(t)
t