PRACTICAL MATLAB® FOR ENGINEERS PRACTICAL MATLAB

462 Practical MATLAB® Applications for Engineers

ANALYTICAL Solution

a. g 1 (n) is nonlinear time invariant

b. g 2 (n) is linear time-varying

c. g 3 (n) is nonlinear

R.5.10 Let us analyze a more complex discrete system, given by the difference equation
g(n) = 4f(n) + 5f(n − 1).
a. Draw the block circuit diagram.
b. Determine its impulse response h(n).

ANALYTICAL Solution

Part a. The circuit block diagram is shown in Figure 5.4.

Part b. The impulse response is evaluated by replacing f(n) with δ(n), yielding the

following:

g(n) = 4 
(n) + 5 
(n − 1)

then

h(n) = 4 
(n) + 5 
(n − 1)

Observe that

i. The system is causal since h(n) = 0, for n < 0.
ii. g(n) depends on f(n) and preceding value of f(n).
iii. The system is stable, BIBO.
iv. The energies associated with the input sequence f(n) and output sequence g(n) are
fi nite.

R.5.11 In general, a causal discrete-time invariance linear systems (LTI) can be described
by a difference equation of the form

gn()agn 12 (1)agn(2)
 a gn NN ( 
) b f n 012 ()bf n(1)b f n(2)


 bfn MM ()

FIGURE 5.4
Discrete-system block diagram of R.5.10.

f(n) g(n)

f(n)

g(n)

L

Z−^1

+

4

5