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.