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Sampling and Reconstruction of Analog Signals 95
1
Reconstructed Signal from x1(n) using zero–order–hold
xa(t)
xa(t)
0.8
0.6
0.4
0.2
0
–5 –4 –3 –2 –1 0 1 2 3 4 5
t in msec.
1
0.8
0.6
0.4
0.2
Reconstructed Signal from x1(n) using first–order–hold
0
–5 –4 –3 –2 –1 0 1 2 3 4 5
t in msec.
FIGURE 3.18 Signal reconstruction in Example 3.23
The plots are shown in Figure 3.18, from which we observe that the ZOH reconstruction
is a crude one and that the further processing of analog signal is
necessary. The FOH reconstruction appears to be a good one, but a careful
observation near t =0reveals that the peak of the signal is not correctly reproduced.
In general, if the sampling frequency is much higher than the Nyquist
rate, then the FOH interpolation provides an acceptable reconstruction. □
The third approach of reconstruction in MATLAB involves the use
of cubic spline functions. The spline function implements interpolation
between sample points. It is invoked by xa = spline(nTs,x,t), inwhich
x and nTs are arrays containing samples x(n) atnT s instances, respectively,
and t array contains a fine grid at which x a (t) values are desired.
Note once again that it is not possible to obtain an exact analog x a (t).
□ EXAMPLE 3.24 From the samples x 1(n) and x 2(n) inExample 3.19, reconstruct x a(t) using the
spline function. Comment on the results.
Solution
This example is similar to Examples 3.21 and 3.22. Hence sampling parameters
are the same as before.
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