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

−

−−−