20
Practical MATLAB
® Applications for Engineers
R.1.52 The family of time-shifted sinc functions are given by
sinc n (t) = sin(t − n)/[(t − n)]
for n = 0, ±1, ±2, …, ±∞ forms and orthonormal family, over the range −∞ ≤ t ≤ +∞,
and are referred to as the sinc family.
R.1.53 The fi rst fi ve members of the sinc family are given as follows:
sinc 0 (t) = sin(t)/[t]
sinc 1 (t) = sin(t − )/[(t − )]
sinc 2 (t) = sin(t − 2)/[(t − 2)]
sinc 3 (t) = sin(t − 3)/[(t − 3)]
sinc 4 (t) = sin(t − 4)/[(t − 4)]
The script fi le sinc_n, shown as follows, returns the plot of the fi rst four members of
the sinc family, over the range −5π ≤ t ≤ +5π, indicated in Figure 1.20.
MATLAB Solution
% Script file: sinc _ n
t =-5*pi: 0.25:5*pi;
Sinc _ 0 = sin(t) ./ (pi*t);
Sinc _ 1 = sin(t- pi ) ./ (pi*(t-pi));
Sinc _ 2 = sin(t- 2*pi ) ./ (pi*(t-2*pi));
Sinc _ 3 = sin(t-3*pi ) ./ (pi*(t-3*pi));
plot(t,Sinc _ 0,’*:’,t,Sinc _ 1,’d-.’,t,Sinc _ 2,’h--’,t,Sinc _ 3,’s-’)
xlabel(‘time’)
ylabel(‘Amplitude’)
title(‘First four members of the sinc family’)
legend(‘sinc 0’,’sinc 1’,’sinc 2’,’sinc 3’)
FIGURE 1.20
(See color insert following page 374.) Plots of the sinc family of R.1.53.
0.35
0.3
0.25
0.2
0.15
0.1
0.05
−0.05
−0.1
0
Amplitude
−20
−15
−10
−5
0
5
1 0
1 5
2 0
time
sinc 0
sinc 1
sinc 2
sinc 3
First four members of the sinc family
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7/25/2008 4:16:14 PM
7/25/2008 4:16:14 PM