Signals and Systems - Electrical Engineering

446 CHAPTER 7: Sampling Theory

The binary signal corresponding to the quantized signal is computed using the functioncoderwhich

assigns the binary codes ’10’,’11’,’00’, and ’01’ to the four possible levels of the quantizer. The result is

a sequence of 0s and 1s, each pair of digits sequentially corresponding to each of the samples of the

quantized signal. The following is the function used to effect this coding.

function z1 = coder(y,delta)

% Coder for 4-level quantizer

% input: y quantized signal

% output: z1 binary sequence

% USE z1 = coder(y)

%

z1 = ’00’; % starting code

N = length(y);

for n = 1:N,

y(n)

if y(n) == delta

z = ’01’;

elseif y(n) == 0

z = ’00’;

elseif y(n) == -delta

z = ’11’;

else

z = ’10’;

end

z1 = [z1 z];

end

M = length(z1);

z1 = z1(3:M) % get rid of starting code

7.5 What Have We Accomplished? Where Do We Go from Here?....................

The material in this chapter is the bridge between analog and digital signal processing. The sampling

theory provides the necessary information to convert a continuous-time signal into a discrete-time

signal and then into a digital signal with minimum error. It is the frequency representation of an

analog signal that determines the way in which it can be sampled and reconstructed. Analog-to-

digital and digital-to-analog converters are the devices that in practice convert an analog signal into

a digital signal and back. Two parameters characterizing these devices are the sampling rate and the

number of bits each sample is coded into. The rate of change of a signal determines the sampling

rate, while the precision in representing the samples determines the number of levels of the quantizer

and the number of bits assigned to each sample.

In the following chapters we will consider the analysis of discrete-time signals, as well as the analysis

and synthesis of discrete systems. The effect of quantization in the processing and design of systems