Discrete and Digital Signals and Systems - Digital Signal Processing: An Introduction with MATLAB and Applications - page 63

Chapter 2
Discrete and Digital Signals and Systems
2.1 Introduction
Before an analog signal can be processed with a digital computer chip, the signal
need to be converted into digital form.
The first phase of the digitization process is to sample the analog signal at
discrete time instants t = nT s , where n is an integer (1, 2, 3,…) and where T s is the
sampling period (i.e., the time interval between successive samples). Note that this
kind of sampling is uniform in the sense that T s is constant, and the sampling
frequency is also constant at f s = 1/T s . The result of sampling an analog signal in
this fashion is a discrete-time signal, also known as a pulse amplitude modulation
(PAM) signal.It should be noted that while uniform sampling is simple and
intuitively appealing, it is not always the most suitable way to perform sampling.
Non-uniform sampling can in some cases actually increase the range of frequen-
cies which can be processed. Nonetheless, for the sake of simplicity, this topic will
focus only on uniformly sampled signals.
The second phase of the digitization process is to quantize the discrete-time
signal. The term quantization refers to the approximation of the sampled analog
values using a finite set of values. For example, in M-bit quantization there are 2 M
allowable levels, and the signal amplitude must be approximated to one of these
levels. If, for example, the expected analog voltage limits are ±3 volts, the input
signal can be quantized in steps of D ¼ 6 = 2 M volts. Typically the voltage quan-
tization levels are chosen to be symmetric around 0 volts.
In the quantization process approximation via rounding or truncation normally
occurs and some information is lost. The quantized signal therefore consists of a
true signal plus an error signal which is referred to as quantization noise. The
power of this noise is dependent on the quantization step, D; with this power being
given by D 2 = 12 (see Sect. 3.6.1.1 ).
The third phase of the digitization process involves an encoding of the multibit
binary sequence into a practical and convenient form before it is used or trans-
mitted. This process is known as pulse code modulation (PCM), and the resulting