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96 Chapter 3 THE DISCRETE-TIME FOURIER ANALYSIS
1
Reconstructed Signal from x1(n) using cubic spline function
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 x2(n) using cubic spline function
0
–5 –4 –3 –2 –1 0 1 2 3 4 5
t in msec.
FIGURE 3.19 Reconstructed signal in Example 3.24
MATLAB script:
% a) Discrete-time Signal x1(n): Ts = 0.0002
>> Ts = 0.0002; n = -25:1:25; nTs = n*Ts; x = exp(-1000*abs(nTs));
% Analog Signal reconstruction
>> Dt = 0.00005; t = -0.005:Dt:0.005; xa = spline(nTs,x,t);
% check
>> error = max(abs(xa - exp(-1000*abs(t))))
error = 0.0317
The maximum error between the reconstructed and the actual analog signal is
0.0317, which is due to the nonideal interpolation and the fact that x a(t) is
nonband-limited. Comparing this error with that from the sinc (or ideal) interpolation,
we note that this error is lower. The ideal interpolation generally suffers
more from time-limitedness (or from a finite number of samples). From the
top plot in Figure 3.19 we observe that visually the reconstruction is excellent.
MATLAB script:
% Discrete-time Signal x2(n): Ts = 0.001
>> Ts = 0.001; n = -5:1:5; nTs = n*Ts; x = exp(-1000*abs(nTs));
% Analog Signal reconstruction
>> Dt = 0.00005; t = -0.005:Dt:0.005; xa = spline(nTs,x,t);
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