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

316 SAMPLING AND ANALOG-TO-DIGITAL CONVERSION
xlabel ('time (sec . )');
% send the signal through a 16-level uniform quantizer
[s_out ,sq__out , sqh_out2 ,Delta, SQNR] =sampandquant (xsig, 4,td, ts) ;
% obtained the PCM signal which is
% - sampled, quantized, and zero-order hold signal sqh_out
% plot the original signal and the PCM signal in time domain
subplot (212 ) ;sfig2=plot (t,xsig, 'k' ,t, sqh_out2 (1:Lsig) , 'b');
set (sfig2 , 'Linewidth ' ,2) ;
title ('Signal {\it g} ({\it t}) and its 4 level PCM signal ')
xlabel ('time (sec . )');
Lfft=2 A ceil ( log2 (Lsig) +l) ;
Fmax=l/ (2*td) ;
Faxis=linspace (-Fmax , Fmax,Lfft} ;
SQHl=fftshift (fft ( sqh_outl ,Lfft) );
SQH2=fftshift (fft ( sqh_out2 ,Lfft) );
% Now use LPF to filter the two PCM signals
BW=lO ; %Bandwidth is no larger than lOHz .
H_lpf=zeros (l,Lfft) ;H_lpf (Lfft/2-BW:Lfft/2+BW-1)=1; %ideal LPF
Sl_recv=SQHl .*H_lpf;
% ideal filtering
s_recvl=real (ifft ( fftshift ( Sl_recv) )); % reconstructed f-domain
s_recvl= s_recvl (l:Lsig) ;
% reconstructed t-domain
S2_recv=SQH2 .*H_lpf;
% ideal filtering
s_recv2=real (ifft ( fftshift( S2_recv) ) ); % reconstructed f-domain
s_recv2=s_recv2 (1:Lsig) ;
% reconstructed t-domain
% Plot the filtered signals against the original signal
figure (2)
subplot (211) ;sfig3=plot (t,xsig, 'b-',t, s_recvl , 'b-. ');
legend ('original ','recovered ')
set (sfig3 , 'Linewidth ' ,2} ;
title ('Signal {\it g} ( {\it t} ) and filtered 16-level PCM signal ')
xlabel ( ' time (sec . ) ' ) ;
subplot (212) ;sfig4=plot (t,xsig, 'b-',t, s_recv2 (1:Lsig) , 'b-. ');
legend('original ','recovered ')
set (sfig4 , 'Linewidth ' ,2) ;
title ('Signal {\it g }({\it t} ) and filtered 4-level PCM signal ')
xlabel ( ' time (sec . ) ' ) ;
In the first example, we maintain the 50 Hz sampling frequency and utilize L = l 6
uniform quantization levels. The resulting PCM signal is shown in Fig. 6.42. This PCM
signal can be low-pass-filtered at the receiver and compared against the original message
signal, as shown in Fig. 6.43. The recovered signal is seen to be very close to the original
signal g(t).
To illustrate the effect of quantization, we next apply L = 4 PCM quantization levels. The
resulting PCM signal is again shown in Fig. 6.42. The corresponding signal recovery is given
in Fig. 6.43. It is very clear that smaller number of quantization levels (L = 4) leads to much
larger approximation error.