INTRODUCTION AND TERMINOLOGY
istorically, a signal meant any set of signs, symbols, or physical gesticulations that transmitted information or messages. The first electronic transmission of information was in the form of Morse code. In the most general sense a signal can be embodied in two forms: (1) some measured or observed behavior or physical property of aphenomenon that contains information about that phenomenon or (2) a signal that can be generated by a manufactured system and have the information encoded. Signals can vary over time or space. Our daily existence is replete with the presence of signals, and they occur not only in man-made systems but also in human and natural systems. A simple natural signal is the measurement of air temperatureover time, as shown in Figure 1.1. Study of the fluctuations in temperature informs us about some characteristics of our environment. A much more complex phenomenon is speech. Speech is intelligence transmitted through a variation over time in the intensity of sound waves. Figure 1.2 shows an example of the intensity of a waveform associated with a typical sentence. Each sound has a differentcharacteristic waveshape that conveys different information to the listener. In television systems the signal is the variation in electromagnetic wave intensity that encodes the picture information. In human systems, measurements of heart and skeletal muscle activity in the form of electrocardiographic and electromyographic voltages are signals. With respect to these last three examples, the objective ofsignal analysis is to process these signals in order to extract information concerning the characteristics of the picture, cardiac function, and muscular function. Signal processing has been implemented for a wide variety of applications. Many of them will be mentioned throughout this textbook. Good sources for other applications are Chen (1988) and Cohen (1986).
CHAPTER 1INTRODUCTION AND TERMINOLOGY
FIGURE 1.1 The average monthly air temperature at Recife, Brazil. [Adapted from Chatﬁeld, ﬁg. 1.2, with permission]
FIGURE 1.2 An example of a speech waveform illustrating different sounds. The utterance is “should we chase .” [Adapted from Oppenheim, ﬁg. 3.3, with permission]
1.2 SIGNAL TERMINOLOGY
A time-dependent signal measured at particular points in timeis synonymously called a time series. The latter term arose within the field of applied mathematics and initially pertained to the application of probability and statistics to data varying over time. Some of the analyses were performed on economic or astronomic data such as the Beveridge wheat price index or Wolfer’s sunspot numbers (Anderson, 1971). Many of the techniques that are used currentlywere devised by mathematicians decades ago. The invention of the computer and now the development of powerful and inexpensive computers have made the application of these techniques very feasible. In addition, the availability of inexpensive computing environments of good quality has made their implementation widespread. All of the examples and exercises in and related to this textbook wereimplemented using subroutine libraries or computing environments that are good for a broad variety of engineering and scientific applications (Ebel, 1995; Foster, 1992). These libraries are also good from a pedagogical perspective because the algorithms are explained in books such as those written by Blahut, 1985; Ingle and Proakis, 2000; Press et al., 2002; and Stearns, 2003. Before beginning adetailed study of the techniques and capabilities of signal or time series analysis, an overview of terminology and basic properties of signal waveforms is necessary. As with any field, symbols and acronyms are a major component of the terminology, and standard definitions have been utilized as much as possible (Granger, 1982; Jenkins and Watts, 1968). Other textbooks that will provide complementary...