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94 Chapter 3 THE DISCRETE-TIME FOURIER ANALYSIS
1
Reconstructed Signal from x2(n) Using Sinc Function
0.5
xa(t)
0
–0.5
–5 –4 –3 –2 –1 0 1 2 3 4 5
t in msec.
FIGURE 3.17 Reconstructed signal in Example 3.22
The maximum error between the reconstructed and the actual analog signals is
0.1852, which is significant and cannot be attributed to the nonband-limitedness
of x a(t) alone. From Figure 3.17, observe that the reconstructed signal differs
from the actual one in many places over the interpolated regions. This is the
visual demonstration of aliasing in the time domain.
□
The second MATLAB approach for signal reconstruction is a plotting
approach. The stairs function plots a staircase (ZOH) rendition of the
analog signal, given its samples, while the plot function depicts a linear
(FOH) interpolation between samples.
□ EXAMPLE 3.23 Plot the reconstructed signal from the samples x 1(n) inExample 3.19 using the
ZOH and the FOH interpolations. Comment on the plots.
Solution
Note that in this reconstruction we do not compute x a(t) but merely plot it
using its samples.
% Discrete-time Signal x1(n) : Ts = 0.0002
>> Ts = 0.0002; n = -25:1:25; nTs = n*Ts; x = exp(-1000*abs(nTs));
% Plots
>> subplot(2,1,1); stairs(nTs*1000,x);
>> xlabel(’t in msec.’); ylabel(’xa(t)’)
>> title(’Reconstructed Signal from x1(n) using zero-order-hold’); hold on
>> stem(n*Ts*1000,x); hold off
%
% Discrete-time Signal x2(n) : Ts = 0.001
>> Ts = 0.001; n = -5:1:5; nTs = n*Ts; x = exp(-1000*abs(nTs));
% Plots
>> subplot(2,1,2); plot(nTs*1000,x);
>> xlabel(’t in msec.’); ylabel(’xa(t)’)
>> title(’Reconstructed Signal from x2(n) using zero-order-hold’); hold on
>> stem(n*Ts*1000,x); hold off
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