B. P. Lathi, Zhi Ding - Modern Digital and Analog Communication Systems-Oxford University Press (2009)

312 SAMPLING AND ANALOG-TO-DIGITAL CONVERSION
set (sfiglc, 'Linewidth ' ,1); title ('Spectrum of {\it g }_T ({\ it t}) ');
% calculate the reconstructed signal from ideal sampling and
% ideal LPF
% Maximum LPF bandwidth equals to BW= floor ((Lfft/Nfactor) /2) ;
BW=l0; %Bandwidth is no larger than l0Hz .
H_lpf=zeros (l,Lfft) ;H_lpf (Lfft/2-BW:Lfft/2+BW-1)=1; %ideal LPF
S_recv=Nfactor*S_out . *H_lpf ;
% ideal filtering
s_recv=real (ifft ( fftshift (S_recv) ));
% reconstructed £-domain
s_recv=s_recv (l:Lsig) ;
% reconstructed t-domain
% plot the ideally reconstructed signal in time
% and frequency domain
figure (2)
subplot (211) ; sfig2a=plot (Faxis,abs ( S_recv) );
xlabel ('frequency (Hz) ');
axi s ([-150 150 0 300] );
title ('Spectrum of ideal filtering (reconstruction) ');
subplot (212 ) ; sfig2b=plot (t,xsig, 'k-.' ,t, s_recv(l:Lsig) , 'b');
legend ('original signal ','reconstructed signal ');
xlabel ('time (sec) ');
title ('original signal versus ideally reconstructed signal ');
set ( sfig2b, 'Linewidth ' , 2) ;
% non-ideal reconstruction
ZOH=ones (l,Nfactor) ;
s_ni=kron ( downsample (s_out ,Nfactor) ,ZOH ) ;
S_ni =fftshift (fft (s_ni ,Lfft) );
S_recv2 =S_ni .*H_lpf;
% ideal filtering
s_recv2=real (ifft ( fftshift (S_recv2 ))); % reconstructed £-domain
s_recv2 =s_recv2 (1:Lsig) ;
% reconstructed t-domain
% plot the ideally reconstructed signal in time
% and frequency domain
figure (3)
subplot (211) ; sfig3a=plot (t,xsig, 'b',t,s_ni (l:Lsig) , 'b');
xlabel ('time (sec) ');
title ('original signal versus flat-top reconstruction ');
subplot (212 ) ; sfig3b=plot (t,xsig, 'b' ,t, s_recv2 (1:Lsig) , 'b--');
legend ('original signal ','LPF reconstruction ');
xlabel ('time (sec) ');
set ( sfig3a, 'Linewidth ' , 2) ; set (sfig3b, 'Linewidth ' , 2) ;
title ('original and flat-top reconstruction after LPF');
To construct the original signal g (t) from the impulse sampling train gT (t), we applied an
ideal low-pass filter with bandwidth 10 Hz in the frequency domain. This corresponds to the
interpolation using the ideal sine function as shown in Sec. 6.1.1. The resulting spectrum, as
shown in Fig. 6.40, is nearly identical to the original message spectrum of g(t). Moreover, the
time domain signal waveforms are also compared in Fig. 6.40 and show near perfect match.
In our last exercise in sampling and reconstruction, given in the same program, we use
a simple rectangular pulse of width T s (sampling period) to reconstruct the original signal
from the samples (Fig. 6.41). A low-pass filter is applied on the rectangular reconstruction
and also shown in Fig. 6.41. It is clear from comparison to the original source signal that the