18
Practical MATLAB
® Applications for Engineers
The fi rst members of the Hermitian family are indicated as follows:
Her 1 = te
−t^2/4
Her 2 = (t
2
− 1) e
−t^2/4
Her 3 = (t
3
− 3t) e
−t^2/4
Her 4 = (t
4
− 6t
2
+ 3) e
−t^2/4
R.1.49 The polynomial factors in the expressions defi ned by Her n are referred as the Hermitian polynomials, and the orthogonal interval is over the range −∞ ≤ t ≤ +∞. The
script fi le Hermite, given as follows, returns the plots of the fi rst fi ve members of the
Hermite’s family, over the range −5 ≤ t ≤ +5, in Figure 1.18.
MATLAB Solution
% Script file: Hermite
t =-5:.1:5;
Her _ 0 = exp(-t.^2./4);
Her _ 1 = t.*exp(-t.^2./4);
Her _ 2 = (t.^2-1).*exp(-t.^2./4);
Her _ 3 = (t.^3-3.*t).*exp(-t.^2./4);
Her _ 4 = (t.^4-6*t.^2+3).*exp(-t.^2./4);
plot(t,Her _ 0,’*:’,t,Her _ 1,’d-.’,t,Her _ 2,’h--’,t,Her _ 3,’s-’,t,Her _ 4,’p:’)
xlabel(‘time’)
ylabel(‘ Amplitude’)
title(‘First five members of the Hermite family’)
legend(‘Her 0’,’Her 1’,’Her 2’,’Her 3’,’Her 4’)
First five members of the Hermite family
4
3
2
1
0
−1
−2
−3
−4
−5
−4
−3
−2
−1
0
1
2
3
4
5
time
Her 0
Her 1
Her 2
Her 3
Her 4
Amplitude
FIGURE 1.18
(See color insert following page 374.) Plots of the Hermite family of R.1.49.
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7/25/2008 4:16:13 PM
7/25/2008 4:16:13 PM