Time Domain Representation of Continuous and Discrete Signals 3
deterministic such as current, voltage, power, or energy represented as vectors or matrices
by MATLAB®.
In this book, following the widely accepted industrial standards, signals are classifi ed
in two broad categoriesAnalog
DiscreteAnalog signals are signals capable of changing at any time. This type of signals is also
referred as continuous time signals, meaning that continuous amplitude imply that the
amplitude of the signal can take any value.
Discrete time signals, however, are signals defi ned at some instances of time, over a time
interval t ∈ [t 0 , t 1 ]. Therefore discrete signals are given as a sequence of points, also called
samples over time such as t = nT, for n = 0, ±1, ±2, ..., ±N, whereas all other points are
undefi ned.
An analog or continuous signal is denoted by f(t), whereas a discrete signal is represented
by f(nT) or in short without any loss of generality by f(n), as indicated in Figure 1.1 by dots.
An analog signal f(t) can be converted into a discrete signal f(nT) by sampling f(t) with a
constant sampling rate T (a time also referred as Ts), where n is an integer over the range
−∞ < n < +∞ large but fi nite. Therefore a large, but fi nite number of samples also referred
to as a sequence can be generated. Since the sampling rate is constant (T), a discrete signal
can simply be represented by f(nT) or f(n), without any loss of information (just a scaling
factor of T).
Continuous time systems or signals usually model physical systems and are best
described by a set of differential equations. The analogous model for discrete models is
described by a set of difference equations.
Signals that occur in nature are usually analog, but if a signal is processed by a computer
or any digital device the continuous signal must be converted to a discrete sequence (using
an analog to digital converter, denoted by A/D), or mathematically by a fi nite sequence of
numbers that represent its amplitude at the sampling instances.
Discrete signals take the value of the continuous signals at equally spaced time intervals
(nT). Those values can be considered an ordered sequence, meaning that the discrete sig-
nal represents mathematically the sequence: f(0), f(1), f(2), f(3), ..., f(n).
The spacing T between consecutive samples of f(t) is called the sampling interval or the
sampling period (also referred to as Ts).•
•
0510Analog signaltf(t)012 3456 789100510Discrete signalnf(n)FIGURE 1.
Analog and discrete signal representation.