Introduction to signals - Continuous and Discrete Time Signals and Systems - page 5

plots the readings of the thermometer as a function of discrete time. In the
aforementioned examples of Fig. 1.1, the RLC circuit, audio recorder, CCD
camera, and thermometer represent different systems, while the information-
bearing waveforms, such as the voltage, audio, charges, and fluctuations in
resistance, represent signals. The output waveforms, for example the voltage in
the case of the electrical circuit, current for the microphone, and the fluctuations
in the resistance for the thermometer, vary with respect to only one variable
(time) and are classified as one-dimensional (1D) signals. On the other hand,
the charge distribution in the CCD panel of the camera varies spatially in two
dimensions. The independent variables are the two spatial coordinates ( m , n ).
The charge distribution signal is therefore classified as a two-dimensional (2D)
signal.
The examples shown in Fig. 1.1 illustrate that typically every system has one
or more signals associated with it. A system is therefore defined as an entity
that processes a set of signals (called the input signals) and produces another
set of signals (called the output signals). The voltage source in Fig. 1.1(a),
the sound in Fig. 1.1(c), the light entering the camera in Fig. 1.1(e), and the
ambient heat in Fig. 1.1(g) provide examples of the input signals. The voltage
across capacitor C in Fig. 1.1(b), the voltage generated by the microphone in
Fig. 1.1(d), the charge stored on the CCD panel of the digital camera, displayed
as an image in Fig. 1.1(f), and the voltage generated by the thermistor, used to
measure the room temperature, in Fig. 1.1(h) are examples of output signals.
Figure 1.2 shows a simplified schematic representation of a signal processing
system. The system shown processes an input signal x ( t ) producing an output
y ( t ). This model may be used to represent a range of physical processes includ-
ing electrical circuits, mechanical devices, hydraulic systems, and computer
algorithms with a single input and a single output. More complex systems have
multiple inputs and multiple outputs (MIMO).
Despite the wide scope of signals and systems, there is a set of fundamental
principles that control the operation of these systems. Understanding these basic
principles is important in order to analyze, design, and develop new systems.
The main focus of the text is to present the theories and principles used in
signals and systems. To keep the presentations simple, we focus primarily on
signals with one independent variable (usually the time variable denoted by t
or k ), and systems with a single input and a single output. The theories that we
develop for single-input, single-output systems are, however, generalizable to
multidimensional signals and systems with multiple inputs and outputs.

input
signal

output
signal

system

Fig. 1.2. Processing of a signal
by a system.

1.1 Classification of signals

A signal is classified into several categories depending upon the criteria used
for its classification. In this section, we cover the following categories for
signals: