# Lec 2 - Chapter 1 Introduction to Signals and Systems 1.1...

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Chapter 1 Introduction to Signals and Systems 1.1 Introduction In general, a signal is any function of one or more independent variables that describes some physical behavior. In the one variable case, often the independent variable is time. For example, a speech signal at the output of a microphone as a function of time is an example of an audio signal. Two such signals are shown in Figure 1.1. ! "!! #!! \$!! %!! &!! ’!! (!! )!! *!! "!!! ! " ! !+& ! !+& " ,-./ ! "!! #!! \$!! %!! &!! ’!! (!! )!! *!! "!!! ! " ! !+& ! !+& " ,-./ Figure 1.1: Examples of audio signals. An example of a signal which is a function of two independent variables is an image, which presents light intensity and possibly color as a function of two spatial variables, say x and y . A system in general is any device or entity that processes signals (inputs) and produces other signals (outputs) in response to them. There are numerous examples of systems that we design to manipulate signals in order to produce some desirable outcome. For example, an audio ampliﬁer will receive as input a weak audio signal produced, for example, by a microphone, and will amplify it and possibly shape its frequency content (more on this later) to produce a higher power signal that can drive a speaker. Another system is the stock market where a large number of variables (inputs) aﬀect the daily average value of the Dow Jones Industrial Average Index (and indeed the value of all stocks). Indeed, the value of the Dow Jones Industrial Average Index as a function of time is another example of a signal (an output of an underlying ﬁnancial system in this case). The Dow Jones industrial average closing values over a 100 day period staring on January 5, 2009 is shown in Figure 1.2 as a function of time and it is another example of a signal. 5

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CHAPTER 1. INTRODUCTION TO SIGNALS AND SYSTEMS 6 0 10 20 30 40 50 60 70 80 90 100 6000 7000 8000 9000 10000 Time, Days Closing Value Figure 1.2: The Dow Jones daily average starting January 5, 2009. 1.2 Continuous and Discrete Time Signals There is a variety of signals and systems that we encounter in every day life. In particular, signals can be continuous-time or discrete-time . Continuous-time signals, as the name implies, take values on a continuum in time, whereas discrete-time signals are deﬁned only over a a discrete set of normally equally spaced times. Examples of continuous-time signals are the audio signals at the output of a condenser (electrostatic based) microphone, as those shown in Figure 1.1. An example of a discrete-time signal is the Dow Jones daily average shown in Figure 1.2, which takes values only over discrete times, i.e. at the end of each day. Unlike in the case of Figure 1.2 where the discrete-time signal is plotted as a continuous-time signal by connecting the points with straight lines, in general, discrete-time signals are plotted as shown in Figure 1.3, which plots the Dow Jones daily average over a 50 day period. 0
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Lec 2 - Chapter 1 Introduction to Signals and Systems 1.1...

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