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

t= [O:td :1.]; %time interval of 1 second
xsig=sin (2*pi*t) -sin (6*pi*t) ; % 1Hz+3Hz sinusoids
Lsig=length (xsig) ;
ts=0 .02; %new sampling rate = 50Hz .
Nfact=ts/td;
% send the signal through a 16-level uniform quantizer
Deltal=0.2; % First select a small Delta=0.2 in DM
s_DMoutl=deltamod (xsig,Deltal ,td,ts) ;
% obtained the DM signal
% plot the original signal and the DM signal in time domain
figure (l) ;
subplot (311) ;sfigl=plot (t,xsig, 'k',t, s_DMoutl (l:Lsig) , 'b' );
set (sfigl , 'Linewidth ' , 2);
title ('Signal {\it g} ({\it t}) and DM signal ')
xlabel ('time (sec .) '); axis ([O 1 -2 .2 2.2));
References 319
%
% Apply DM again by doubling the Delta
Delta2=2*Deltal ; %
s_DMout2=deltamod (xsig, Delta2 ,td,ts ) ;
% obtained the DM signal
% plot the original signal and the DM signal in time domain
subplot (312) ;sfig2=plot (t,xsig, 'k' ,t, s_DMout2 (1:Lsig) , 'b');
set (sfig2 , 'Linewidth' , 2);
title ('Signal {\it g} ({\ it t}) and DM signal with doubled stepsize' )
xlabel ('time (sec . )'); axis ( [O 1 -2 .2 2.2 ]);
%
Delta3=2*Delta2 ; % Double the DM Delta again .
s_DMout3=deltamod (xsig, Delta3 ,td,ts ) ;
% plot the original signal and the DM signal in time domain
subplot (313) ;sfig3=plot (t,xsig, 'k' ,t, s_DMout3 (1:Lsig) , 'b');
set (sfig3 , 'Linewidth' ,2) ;
title ('Signal {\it g} ({\it t} ) and DM signal with quadrupled
stepsize')
xlabel ('time (sec . )'); axis ([O 1 -2 .2 2.2));
To illustrate the effect of DM, the resulting signals from the DM encoder are shown in
Fig. 6.44. This example clearly shows that when the step size is too small (i), there is a
severe overloading effect as the original signal varies so fast that the small step size is unable
to catch up. Doubling the DM step size clearly solves the overloading problem in this example.
However, quadrupling the step size (3) would lead to unnecessarily large quantization error.
This example thus confirms our earlier analysis that a careful selection of the DM step size is
critical.
REFERENCES
1. D. A. Linden, "A discussion of sampling theorem," Proc. IRE, vol. 47, no.7, pp. 1219 - 1226,
July 1959.
2. H. P. Kramer, "A Generalized Sampling Theorem," J. Math. Phys. , vol. 38, pp. 68 - 72, 1959.