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1、Signals and Systems,Chapter 1,1.1 Signals,Signals are functions of independent variables that carry information.The independent variables can be continuous or discrete.The independent variables can be 1-D,2-D,n-D.For this course:Focus on a single(1-D)independent variable which we call“time”.Continuo
2、us-Time signals:x(t),t-continuous values.Discrete-Time signals:x(n),n-integer values only.,Examples,Electrical signals voltages and currents in a circuit.Acoustic signals audio or speech signals.Video signals intensity variations in an image.Biological signals sequence of bases in a gene.,A Simple R
3、C Circuit,The patterns of variation over time in the source voltage Vs and capacitor voltage Vc are examples of signals.,A Speech Signal,A Picture,Vertical Wind Profile,1.2 Systems,For the most part,our view of systems will be from an input-output perspective.A system responds to applied input signa
4、ls,and its response is described in terms of one or more output signals.,Example,RLC circuit,By interconnecting simpler subsystems.We can build more complex systems.,1.3 Types of Signals,Example,Noise Signal and Interfere Signal,Example,Periodic Signal,Example,Continuous-time Signal,Example,Discrete
5、-time Signal,Example,1.Sinusoidal Signal,1.4 Typical Signals,2.Real Exponential Signal,4.Sampling Signal,5.Unit Step Signal,6.Unit Impulse Signal,7.Unit Impulse Even Signal,Properties:,8.Unit Triangle Signal,Properties:,1.5 Basal Operation of Signals,3.Time Shift,4.Flexibility,Example,1.6 The Repres
6、entation of Continuous-time Signals in Terms of Impulses,Define:,1.7 Discrete-time Signal,2.Basal Operation of Sequences,(3)Unit Rectangle Sequence,(a)1；(b)01；(c)-10；(d)-1,(6)Sinusoidal Sequence,(a)Growing sinusoidal sequence；(b)Decaying sinusoidal sequence,4.The Representation of Discrete-time Signal in Terms of Unit Samples,1.8 Calculation of Convolution,1.Calculation of Convolution Integral,Example,When t3,2.Calculation of Convolution Sum,Example 1,Solution:,Example 2,DT Signals,
