PRACTICAL MATLAB® FOR ENGINEERS PRACTICAL MATLAB

558 Practical MATLAB® Applications for Engineers

P.5.12 Determine the discrete FS coeffi cients of the following periodic series:

a. f 1 (n) = cos(πn/2)

b. f 2 (n) = sin(πn/2) + cos(πn/3)

P.5.13 Let the causal LTI system equation be g(n) = (1/3)g(n − 1) + 3f(n), with g(n) = 0 for
n ≤ 0.
a. Determine and plot its impulse response h(n) over the range 0 ≤ n ≤ 31 by
simulating the difference equation.
b. Repeat part a for the case of a step response
c. Determine its transfer system function given by H(z) = G(z)/F(z)
d. Repeat parts a and b using the commands impz and dstep
e. Evaluate and plot the system poles and zeros of H(z)
f. Discuss and state if the system is stable by observing the locations of its system
poles
g. Discuss if the system is stable by verifying the BIBO criteria

P.5.14 Use MATLAB and verify the following relations:

a. n
  fn FejW dW





[()]^2 
 ( )

1

2  



∫ Parseval’s theorem

b. fF()^1 ( )0edjW W

2





 



∫ Initial value theorem

c. F()efnj^0 
n
  ()

using the following sequence f(n) = [1 2 3 4 5 6 7 8 9 10].

P. 5. 1 5 L e t f(n) = 0.3n, for n = 0, 1, 2, 3, ..., 8, 9, 10. Use MATLAB to verify the following
relations:
a. f()neFe 2 ⇔ jW^2 ()jW
b. fn Fe( )⇔ (jW) (where * denotes complex conjugate)
c. f() ( )nFe⇔ jW

P.5.16 Evaluate the DTFT, DFT, and ZT of the following sequences:

a. f 1 (n) = 
(n) + 2 
(n − 1) − 3 u(n)

b. f 2 (n) = u(n) − u(n − 10) − 3 r(n)

c. f 3 ()nnunnn
 335 cos( )() 2255 2sin( )+ 
()

P.5.17 Given the difference equation g(n) = − 3 g(n − 1) + 2 g(n − 2) + 5, determine its
system transfer function and indicate if the system is causal and stable.

P.5.18 Given the system transfer function

He

e

ee

jW

jW

() jW j W

.

..









05

(^105052)
determine its system difference equation, system realization, and indicate if the
system is causal and stable.