Time Domain Representation of Continuous and Discrete Signals 97
P. 1. 2 4 L e t f 1 (t) = 3e2t/3 + 3 and f 2 (t) = cos(πt). Create a script fi le that returns the energy and
power of f 1 (t) and f 2 (t).
P.1.25 Repeat P.1.24 for the following discrete sequences: f 1 (n) = 3e2n/3 + 3 and f 2 (n) =
cos(0.1πn), over the range − 10 ≤ n ≤ 10.
P.1.26 Evaluate by hand which of the following discrete sequences are periodic, and if
periodic, evaluate its period.
a. cos(0.2n)
b. cos(0.2πn)
c. sin(2πn/3)
d. sin(9.1n)
P.1.27 Verify the following equalities:
a. Imp[( )]n
()nk
k
∑
b. un[( )]
()nk
k 0
∑
c. rn k n k
k
()( )
0
∑
P.1.28 Evaluate the following integrals:
a. ∫()()23ttdt+ 1
b. ∫()((/))23321ttdt+
c. sin(wt) (( / ) 32 23t ( / ))dt
∫
d. et dt()t ((/))
∫ 31 1 ^23
P.1.29 Analyze and draw a fl ow chart of Example 1.15 and indicate in each average approx-
imation the fi lter used as well as the effect of the fi lter.
P.1.30 Evaluate the fi rst and second derivative of the following expressions:
a. f 1 (t) = u(t) + 7u(t − 5) − 2u(t − 7)
b. f 2 (t) = tu(t) + e3tu(t − 1) + 3 δ(t − 3)
c. f 3 (t) = r(t)u(t) − r(t − 1)u(t − 1)
P. 1. 3 1 L e t H(s) = ___s^ +^3
s^3 + s^2 + 5 s + 10
be the transfer function of a given analog system. Write
a MATLAB program that returns
a. The Bode plot of H(s), magnitude and phase
b. The impulse as well as the step responses
c. The zero/pole diagram
d. The system differential equation
P. 1. 3 2 L e t
Hz
zzz
zzz
()
....
...
032 043 085 02
1 0 802 0 42 0 62
123
123
−
−−−