PRACTICAL MATLAB® FOR ENGINEERS PRACTICAL MATLAB

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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.

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