PRACTICAL MATLAB® FOR ENGINEERS PRACTICAL MATLAB

DTFT, DFT, ZT, and FFT 485

Evaluate the Z[f(n)] in the following ways:

a. Analytically

b. Symbolically by using MATLAB

ANALYTICAL Solution

Fz Z f n f nzn z z

n

()

[ ( )] ( ) 






0

1 1 12

3

1

9

1

∑ 27

























zz

n

 (^3) ^1 n
3


Fz z
z
z
z
() z
(/ ) (/ )





113   13
1
(^13)
for 
MATLAB Solution

syms z n
Fz = ztrans(1/3^n)
Fz =
3z/(3z-1)
pretty(Fz)
z
3 -------
3 z - 1
R.5.77 Let us gain some experience by evaluating the ZT of the following functions by
using MATLAB:
a. f 1 (n) = u(n)
b. f 2 (n) = anu(n)
c. f 3 (n) = cos(an)u(n)
d. f 4 (n) = sin(an)u(n)
e. f 5 (n) = bnsin(an)u(n)
MATLAB Solution
syms a b n
f1 n = 1^n; % part(a)
F1 z = ztrans(f1 n)
F1 z =
z/(z-1)
pretty(F1 _ z)
z

z - 1
f2 n = a^n; % part(b)
F2 z =ztrans(f2 _ n)