Sampling and quantization - Continuous and Discrete Time Signals and Systems - page 393

CHAPTER

9

Sampling and quantization

Part II of the topic covered techniques for the analysis of continuous-time (CT)
signals and systems. In Part III, we consider the corresponding analysis tech-
niques for discrete-time (DT) sequences and systems. A DT sequence may
occur naturally. Examples are the one-dimensional (1D) hourly measurements
x [ k ] made with an electronic thermometer, or the two-dimensional (2D) image
x [ m , n ] recorded with a digital camera, as illustrated earlier in Fig. 1.1. Alter-
natively, a DT sequence may be derived from a CT signal by a process known as
sampling. A widely used procedure for processing CT signals consists of trans-
forming these signals into DT sequences by sampling, processing the resulting
DT sequences with DT systems, and converting the DT outputs back into the
CT domain. This concept of DT processing of CT signals is illustrated by the
schematic diagram shown in Fig. 9.1. Here, the input CT signal x ( t ) is con-
verted to a DT sequence x [ k ]bythe sampling module, also referred to as the
A/D converter. The DT sequence is then processed by the DT system module.
Finally, the output y [ k ] of the DT module is converted back into the CT domain
by the reconstruction module. The reconstruction module is also referred to as
the D/A converter. Although the intermediate waveforms, x [ k ] and y [ k ], are
DT sequences, the overall shaded block may be considered as a CT system
since it accepts a CT signal x ( t ) at its input and produces a CT output y ( t ). If
the internal working of the shaded block is hidden, one would interpret that the
overall operation of Fig. 9.1 results from a CT system.
In practice, a CT signal can either be processed by using a full CT setup,
in which the individual modules are themselves CT systems (as explained in
Chapters 3-8), or by using a CT-DT hybrid setup (as shown in Fig. 9.1). Both
approaches have advantages and disadvantages. The primary advantage of CT
signal processing is its higher speed as DT systems are not as fast as their
counterparts in the CT domain due to limits on the sampling rate of the A/D
converter and the clock rate of the processor used to implement the DT systems.
In spite of its limitation in speed, there are important advantages with DT sig-
nal processing, such as improved flexibility, self-calibration, and data-logging.
Whereas CT systems have a limited performance range, DT systems are more

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