PRACTICAL MATLAB® FOR ENGINEERS PRACTICAL MATLAB

8 Practical MATLAB® Applications for Engineers

The expansion of the function Imp[(t)T] results in

Imp[( ) ] ( )

()()()()

ttnT

tnT tT t tT

T

n

   









∑

...... (()tnT

R.1.15 The sampling process is modeled mathematically by multiplying an arbitrary ana-
log signal f(t) by the train of impulses defi ned by Imp[(t)T]. This process is illustrated
graphically in Figure 1.6.
Analytically,

ft t nT ft t nT

n n

()⋅∑

(
) ∑ () ( )


 











and the expanded discrete version of f(t) is given by

fn fk t k f t f t f t

f

k

()

()( ) ( )( ) ( )( ) ()()









  



∑
22 110

(()(

tft)( )( ) 
 fntn( )(
)112 2

assuming that T = 1 , without any loss of generality.

0

5

10

f(t)

− 4 T − 3 T − 2 T −T 0 T 2 T 3 T 4 T 5 T 6 T

0

0.

1

ImpT(t)

− 4 T − 3 T − 2 T −T 0 T 2 T 3 T 4 T 5 T 6 T

0

5

10

t

f(t)

ImpT(t)*

FIGURE 1.
Plots illustrating the sampling process.