94 Practical MATLAB® Applications for Engineers
P.1.3 Create a script fi le that returns the plots of each of the functions defi ned in P.1.1.
P.1.4 Create a script fi le that returns the plots of each of the sequence defi ned in P.1.2.
P.1.5 Sketch by hand, over the range − 1 ≤ n ≤ 8 , the sequence ƒ(n) = (0.32)n [u(n) −
u(n − 6)].
P.1.6 Let ƒ(n) = (0.32)n [u(n) − u(n − 6)], over − 1 ≤ n ≤ 8.
Write a script fi le that returns the following plots:
a. ƒ(n) versus n
b. ƒ(2n) versus n
c. ƒ(n/2) versus n
d. ƒ(n − 3) versus n
P.1.7 Given the sequence fn m n m
m
()(/) ( )
12
0∑
a. Write a program that returns the plot of ƒ(n) versus n, over the range 0 ≤ n ≤ 30.
b. Evaluate the energy and power of f(n).P.1.8 Given the sequence ƒ(n) = 15(0.75)n u(n). Create the script fi le that returns the plot
of ƒ(n) versus n, over the range − 10 ≤ n ≤ 30.
Observe and discuss if the sequence f(n) diverges or converges.
P.1.9 Given the sequence ƒ(n) = 0.2(1.1)n u(n), create a script fi le that returns the plots of
ƒ(n) versus n, over the range − 10 ≤ n ≤ 30.
Discuss if the sequence f(n) converges or diverges.
P.1.10 Given the following analog signals:
- ƒ 1 (t) = 4e−2t u(t)
- ƒ 2 (t) = 5e−1.5t cost(5t − π/2)u(t)
- ƒ 3 (t) = 6(1 − e−2t)u(t)
- ƒ 4 (t) = e−tcos(5t − π/4)u(t)
(a) Sketch by hand each of the given functions versus t. (b) Write a program that
returns the plots of each of the functions of part (a), over the range − 1 < t < 6.
P.1.11 Write a MATLAB program that returns the plots of the continuous function ƒ(t) =
3 cos(0.15πt) + 2sin(0.20πt), and f(t) sampled with TS = 0. 1 π over the range 0 < t < 15 π.
P.1.12 In general, a random noisy signal of length N can be generated by using the follow-
ing MATLAB command:
Noise=rand(1,N)Likewise, the sequence
Noisen=randn(1,N)returns a random sequence of length N, normally distributed with zero mean and
unit variance. Write a program that returns the plots, the average value, the
maxima, and minima of each of the noisy sequences defi ned earlier for N = 100
and 200.