分析信號與系統(tǒng)chapter1-signals and systems

1、Chapter1Signals And Systems崔琳莉In this chapter, we will learnHow to describe signals ?What are the basic signals we need to know?How to describe systems? How to model them?What are basic systems properties ? Build a mathematical tool for signals and systemsFirst, how to describe signals? Continuous-T

2、ime Signalsi.e. CT signals Discrete-Time Signalsi.e. DT signals1.1 Continuous-Time and Discrete-Time Signals1.1.1 Examples and Mathematical Representation(1) A simple RC circuitSource voltage Vs and Capacitor voltage VcA. Examples(2) An automobileForce f from engineRetarding frictional force VVeloci

3、ty V(3) A Speech Signal(4) A Picture(5) vital statistics(人口統(tǒng)計)NoteIn this book, we focus on our attention on signals involving a single independent variable.For convenience, we will generally refer to the independent variable as time, although it may not in fact represent time in specific applicatio

4、ns.B. Two basic types of signals t: continuous timex(t):continuum of value1. Continuous-Time signal2. Discrete-Time signal n: discrete timexn: a discrete set of values (sequence)Example1: 1990-2002年的某村農(nóng)民的年平均收入SamplingExample2: xn is sampled from x(t)Why DT? (1) Function Representation Example: x(t)

5、= cos0t xn = cos0n x(t) = ej0t xn = ej0n(2) Graphical Representation Example: ( See page before )(3) Sequence-representation for discrete-time signals:xn=-2 1 3 2 1 1 or xn=(-2 1 3 2 1 1)C. RepresentationNote:Since many of the concepts associated with continuous and discrete signals are similar (but

6、 not identical), we develop the concepts and techniques in parallel.There are many other signals classification:Analog vs. DigitalPeriodic vs. Aperiodic Even vs. OddDeterministic vs. Random1.1.2 Signal Energy and PowerInstantaneous power:Let R=1, so +R_Energy : t1tt2Average Power:Total EnergyAverage

7、 PowerDefinition:Continuous-Time:(t1tt2)Discrete-Time:(n1nn2 )We will frequently find it convenient to consider signals that take on complex values.whenTotal EnergyAverage PowerNote:It is important to remember that the terms “Power” and “energy” are used here independently of the quantities actually are related to physical energy.With these definitions, we can identify three important class of signalsa. Finite total energyb. Finite average