7.4 Practical Aspects of Sampling 445%%%%%%%%%%%%%%%%%%%%%%%%%%%
% Sampling, quantization and coding
%%%%%%%%%%%%%%%%%%%%%%%%%%%
clear all; clf
% analog signal
t = 0:0.01:1; x = 4∗sin(2∗pi∗t);
% sampled signal
Ts = 0.01; N = length(t); n = 0:N−1;
xs = 4∗sin(2∗pi∗n∗Ts);
% quantized signal
Q = 2; % quantization levels is 2Q
[d,y,e] = quantizer(x,Q);
% binary signal
z = coder(y,d)The quantization of the sampled signal is implemented with the functionquantizerwhich compares
each of the samplesxs(nTs)with four levels and assigns to each the corresponding level. Notice the
appproximation of the values given by the quantized signal samples to the actual values of the signal.
The difference between the original and the quantized signal, or the quantization error,ε(nTs), is also
computed and shown in Figure 7.13.
function [d,y,e] = quantizer(x,Q)
% Input: x, signal to be quantized at 2Q levels
% Outputs: y quantized signal
% e, quantization error
% d quantum
% USE [d,y,e] = quantizer(x,Q)
%
N = length(x);
d = max(abs(x))/Q;
for k = 1:N,
if x(k)>= 0,
y(k) = floor(x(k)/d)*d;
else
if x(k) == min(x),
y(k) = (x(k)/abs(x(k)))∗(floor(abs(x(k))/d)∗d);
else
y(k) = (x(k)/abs(x(k)))∗(floor(abs(x(k))/d)∗d + d);
end
end
if y(k) == 2∗d,
y(k) = d;
end
end