Fourier and Laplace 401
F10 =10*sin(w*tau10/2)./(w*tau10/2);
subplot(3,1,1)
plot(w,F1);
ylabel(‘Amplitude’);
title(‘Spectrum of pulse with tau=1’);
axis([-10 10 -1 2]);
subplot(3,1,2);plot(w,F5);
ylabel(‘Amplitude’);
title(‘Spectrum of pulse with tau=5’);
axis([-7 8 -4 6]);
subplot(3,1,3);plot(w,F10);
xlabel(‘frequency w (in rad/sec)’);
ylabel(‘Amplitude’);
title(‘Spectrum of pulse with tau=10’);
axis([-10 10 -4 11]);
The script fi le square_FT_num is executed and the results are as follows (Figure 4.50):
>> square _ FT _ num
frequency w (in rad/sec)
frequency w (in rad/sec)
(Numerical solutions)
Spectrum of pulse with τ = 1
2
0
6
4
2
− 2
− 4
0
1
− 1
− 10
10
5
0
− 8 − 6
− 6
− 10 − 8 − 6 − 4 − 202
− 4
− 4
− 2
− 2
0
0
2
2
4
4
6
6
8
8
10
Spectrum of pulse τ = 5
Spectrum of pulse τ = 10
frequency w (in rad/sec)
4 6810
Amplitude
Amplitude
Amplitude
FIGURE 4.50
Numerical plots of part 2 of Example 4.8.