730 CHAPTER 12: Applications of Discrete-Time Signals and Systems
types—developed into time-division multiplexing (TDM), which is the dual of frequency-division
multiplexing (FDM). In TDM, samples from different messages are interspersed into one message
that can be quantized, coded, and transmitted and then separated into the different messages at the
receiver.
As multiplexing techniques, FDM and TDM became the basis for similar techniques used in wireless
communications. Typically, three forms of sharing the available radio spectrum are: frequency-
division multiple access (FDMA) where each user is assigned a band of frequencies all of the time;
time-division multiple access (TDMA) where a user is given access to the available bandwidth for
a limited time; and code-division multiple axis (CDMA) where users share the available spectrum
without interfering with each other thanks to a unique code given to each user.In this section we will introduce some of these techniques avoiding technical details, which we leave
to excellent books in communications, telecommunications, and wireless communications. As you
will learn, digital communications has a number of advantages over analog communications:n The cost of digital circuits decreases as digital technology becomes more prevalent.
n Data from voice and video can be merged with computer data and transmitted over a common
transmission system.
n Digital signals can be denoised easier than analog signals, and errors in digital communications
can be corrected using special coding.However, digital communication systems require a much larger bandwidth than analog communica-
tion systems, and quantization noise is introduced when transforming an analog signal into a digital
signal.12.4.1 Pulse Code Modulation
PCM can be seen as an implementation of analog-to-digital conversion of analog signals providing
a serial bit stream. This means that sampling applied to a continuous-time message gives a pulse
amplitude–modulated (PAM) signal that is then quantized and assigned a binary code to differentiate
the different quantization levels. If each of the digital words hasbbinary digits, there are 2blevels,
and to each a different code word is assigned. An example of a code commonly used is the Gray code
where only one bit changes from one quantization level to another. The most significant bit can be
thought to correspond to the sign of the signal (1 for positive values, and 0 for negative values) and
the others differentiate each level.PCM is widely used in digital communications given that:n It is realized with inexpensive digital circuitry.
n It allows merging and transmission of data from different sources (audio, video, computers, etc.)
by means of time-division multiplexing, which we will see next.
n PCM signals can be easily regenerated by repeaters in long-distance digital telephony.Despite all of these advantages, you need to remember that because of the sampling and the quan-
tization the process used to obtain PCM signals is neither linear nor time invariant, and as such