数字信号处理英文版

1、Digital Signal ProcessingUnderstanding DSP, Second Edition数字信号处理（第二版（英文版） 作译者：张建华,教材Understanding DSP, Second Edition参考书:1. 数字信号处理教程(第二版） 程佩青 2. 数字信号处理 丁玉美 Understanding DSP, Second Edition3. S. K. Mitra, Digital signal processing a computer-based approach, second edition, Copyright 2001 by McGraw-H

2、ill CompUnderstanding DSP, Second Edition The field of DSP has grown to be important both theoretically and technologically.Development and use of low-cost software and hardwareNew tech. and app. take advantage of DSP algorithmsMake DSP an integral part of any E.E. curriculumUnderstanding DSP, Secon

3、d EditionLearning digital signal processing is not something you accomplish; its a journey you take. When you gain an understanding of some topic, questions arise that cause you to investigate some other facet of digital signal processing. Armed with more knowledge, youre likely to begin exploring f

4、urther aspects of digital signal processing. The book is your tour guide during your first steps of your journey. -Richard G. LyonsUnderstanding DSP, Second Edition7Chapter 1 Discrete Sequences and SystemsUnderstanding DSP, Second Edition8Outline1.1 Discrete Sequences and Their Notation1.2 Signal Am

5、plitude, Magnitude, Power1.3 Signal Processing Operational Symbols1.4 Introduction to Discrete Linear Time-Invariant Systems1.5 Discrete Linear Systems1.6 Time-Invariant Systems1.7 The Commutative Property of Linear Time-Invariant Systems1.8 The Causality Property of Linear Time-Invariant Systems1.9

6、 The Stability Property of Linear Time-Invariant Systems1.10 Analyzing Linear Time-Invariant SystemsUnderstanding DSP, Second Edition1.1.1 Discrete-time SignalsContinuous-Time (CT) signals: - All CT signals are thought of as a pattern of variations in time and represented as a time function x(t).- d

7、efined at every time instant.Understanding DSP, Second EditionUnderstanding DSP, Second Edition1.1.1 Discrete-time SignalsDiscrete-Time(DT) Signals:- Defined at discrete time instants.- A discrete-time signal is represented as a sequence of numbers called samples and can be mathematically denoted as

8、 such a setn-nx , )(Understanding DSP, Second Edition121.1.1 Discrete-time Signalsx(n): n: index, integer in the range - and +, x(n) is one sampleE.g.x(-1)=-0.1564;x(0)=0;x(1)=0.1564;x(2)=0.3090;Understanding DSP, Second Edition- Most DT signal are obtained by sampling continuous-time signals.1.1.1

9、Discrete-time SignalsUnderstanding DSP, Second Edition141.1.1 Discrete-time Signalsx(n)comes from: xa(t)=sin(2ft)Uniformed sampled as:xa(nT)=sin(2fnT)T denotes sampling interval or period and its reciprocal is sampling frequency written as:sampling frequencyUnderstanding DSP, Second Edition151.1.1 D

10、iscrete-time SignalsRelationship between xa(nT) and xa(t):Part and whole;Under certain conditions, xa(t) can be exclusively reconstructed based on xa(nT).Understanding DSP, Second Edition161.1.1 Discrete-time SignalsAbout Sequence:x(n) is a real sequence if x(n) is real for any n.x(n) is a complex s

11、equence if x(n) is complex.x(n) = xre(n) + jxim(n)x(n) is a finite length sequence if it is defined only for a finite time interval as: N1nN2.The length of a finite length sequence is:N= N2-N1+1: N point sequenceUnderstanding DSP, Second Edition171.1.1 Discrete-time SignalsAbout Sequence:x(n) is a i

12、nfinite length sequence if it is defined for infinite time interval.(By appending with zeros or zero-padding, finite length sequence infinite.)Three types of infinite length sequence, as: Right-side sequenceUnderstanding DSP, Second Edition181.1.1 Discrete-time SignalsLeft-side sequenceTwo-side sequ

13、ence: -nLeft-side sequenceUnderstanding DSP, Second Edition1919(1) Unit sample sequencediscrete-time impulseunit impulseShifted:1.1.2 Frequently Used Discrete Sequences1,0( )0,0nnn0001,()0,nnnnnn( )n01( )n-201Understanding DSP, Second Edition2020For any sequence could be expressed as the weighted su

14、m of:shifted unit sample sequences1.1.2 Frequently Used Discrete Sequences( )( )( )( )( )0( )1 (1)2(2)()kx nxnxnxnx kn k Important! Often used laterUnderstanding DSP, Second Edition Understanding DSP, Second Edition)2()2()()0() 1() 1 ()(nxnxnxnx Understanding DSP, Second Edition23231.1.2 Frequently

15、Used Discrete Sequences()1,00,0nunn( ( ) ) n un01(2) Unit step sequenceUnderstanding DSP, Second Edition24241.1.2 Frequently Used Discrete SequencesRelation between u(n) and (n)(n) could be expressed as：u(n) could be expressed as：( )( )(1)nu nu n( )0()( )(1)(2)ku nnknnnUnderstanding DSP, Second Edit

16、ion25251.1.2 Frequently Used Discrete Sequences(3) Rectangular sequence( )NnnNnnRN, 0,010, 1( ( ) )nRNn01 NUnderstanding DSP, Second Edition26261.1.2 Frequently Used Discrete SequencesRelation of RN(n), u(n) and (n)RN(n) is expressed as:RN(n) is expressed as:( )( )()NRnu nu nN( )10()( )(1)(1)NNkRnnk

17、nnnNUnderstanding DSP, Second Edition27271.1.2 Frequently Used Discrete Sequences(4) Real exponential sequencewhen 0a 0, shift to right This is not a LTI system.Understanding DSP, Second Edition46461.7 The Commutative Property of Linear Time-Invariant SystemsSwapping the order of two cascaded system

18、s does not alter the final output.Understanding DSP, Second EditionCausal Systems A system is said to be causal if its current output depends only on its current and past inputs.For Examples: (1) The first-order forward difference system (noncausal) (2) The first-order backward difference system (ca

19、usal)() 1()(nxnxny) 1()()(nxnxnyn0ny 1.8 The Causality Property of Linear Time-Invariant SystemsUnderstanding DSP, Second Edition48481.8 The Causality Property of Linear Time-Invariant Systems For the causal system, if x1(n)=x2(n) for nn0, then y1(n)=y2(n) for nn0.Causality:If a LTI system is a caus

20、al system, it satisfies:Realizable System, it is used to prove the causality of the system (Important).Understanding DSP, Second Edition49491.8 The Causality Property of Linear Time-Invariant SystemsCausality:If a LTI system is a causal system, it satisfies:Realizable System, it is used to prove the

21、 causality of the system (Important).Understanding DSP, Second Edition50501.9 The Stability Property of Linear Time-Invariant SystemsStability:If and only if for every bounded input, the output is also bounded (BIBO).i.e.ThenIn the later discussion, the involved discrete system is the LTI system. Ge

22、neral practical systems are causal and stable.Understanding DSP, Second Edition51511.9 The Stability Property of Linear Time-Invariant SystemsSignificant Conclusion:For a LTI system, the sufficient but not necessary condition to stability is:Understanding DSP, Second Edition52521.9 The Stability Pro

23、perty of Linear Time-Invariant SystemsProof:Because, assuming |x(n)|M.Understanding DSP, Second Edition53531.10 Analyzing Linear Time-Invariant SystemsKnowing the (unit) impulse response of an LTI system, we can determine the systems output sequence for any input sequence because the output is equal

24、 to the convolution of the input sequence and the systems impulse response. Understanding DSP, Second EditionPeriodicity of SequencesFor Real Sinusoidal Sequences Ifis periodic, thenThus,We assume, without loss of generality, that the frequency is restricted in the range of The fundamental period ca

25、n be found bywhere is a smallest positive integer. How to identify whether a real sinusoidal sequence is periodic? ),cos()(0nnAnxkN20 ,)(cos)()(0nNnANnxnx. 20mink/N)2(0mink0Understanding DSP, Second EditionPeriodicity of Sequences (1) If is a positive integer, then the sequence is periodic and (2) I

26、f where positive integers and are mutually prime, then the sequence is periodic and (3) If is a nonrational number, then the sequence is not periodic. For the complex exponential sequence, the discussion of its periodicity is the same as that of the real sinusoidal sequence. )2(0/) 1 choosing (mink)

27、2(0/NP/Q/)2(0QP) choosing (PkminQN )2(0/Understanding DSP, Second EditionPeriodicity of Sequences Furthermore, the parameter , no matter how a sinusoidal or complex exponential sequence is periodic or nonperiodic, is always called the frequency of the sequence.Example 2.3 A real sinusoidal sequence

28、is given by with , radians and . Determine N . Solution: Substituting parameters into the given sequence, we haveBecause is an integer, the sequence is periodic and its fundamental period is . In fact, It means that one cycle of the sequence consists of 8 samples:0 ),cos()(0nnAnx1A )4(0/0n-/nnx ),4c

29、os()(8)2(0/8N n ),()4cos()8(4cos)8(nxnnnxUnderstanding DSP, Second EditionPeriodicity of SequencesUnderstanding DSP, Second EditionWhy signals should be processed?Signals are carriers of information-Useful and unwanted-Extracting, enhancing, storing and transmitting the useful informationHow signals

30、 are being processed?- Analog Signal Processing - Digital Signal Processing Understanding DSP, Second EditionDigital Signal Processing the processing or manipulation of signals using digital techniquesADCDACDigital Signal ProcessorAnalogue to Digital ConverterDigital to Analogue ConverterInput Signa

31、lOutput SignalUnderstanding DSP, Second EditionThe foundation of information technology is digitalization.The kernel of digitalization is digital signal processingUnderstanding DSP, Second EditionMost of digital signal processing, especially real-time processing are implemented by DSP processor or A

32、SIC based on DSP core DSP technology becomes hot front edge and is growing up rapidly.Understanding DSP, Second EditionWhat is DSP Used For?And much more!Understanding DSP, Second EditionDSP used in a wide range of everyday applicationsLooked at:Speech coding; Speech synthesis & recognition;Imag

33、e/Video;Adaptive filtering.Other areas include:Image analysis (e.g. face recognition, OCR, etc.);RADAR/SONAR;Data transmission and reception;And many more.!Understanding DSP, Second Edition Why digital? （1）Programmability Analog system：Modify hardware design.Digital system：Modify software.Example：An

34、alog filter, digital filter, adaptive filter （2）Precision Analog system：component specification: resistors have a tolerance 5%; capacitors 20% or worseDigital system：ADC bits, CPU word width and algorithmUnderstanding DSP, Second Edition（3）Stability Analog system：the characteristics of analog system

35、 components, resistors, capacitors and operational amplifiers will change along with temperature, humidityDigital system：will show no variation with temperature throughout their guaranteed operation range.Understanding DSP, Second Edition(4) Anti-noiseDigital signals are less susceptible to noise an

36、d disturbance. Understanding DSP, Second Edition(5) Repeatability Understanding DSP, Second Edition(6) Error Correcting CodesData retrieval and transmission systems suffer from a number of potential forms of error.With information in a digital or binary form, we may easily build into the data stream

37、 additional “redundant” bits that are used to detect when an error has occurred.Understanding DSP, Second Edition(7) Data Transmission and Storage The Internet, Compact Disc (CD) and Digital Video Disc (DVD) brought information based on trouble-free high-quality text, audio and video into the office and home. The fidelity of the digital medium is greater than that of the analog one.Understanding DSP, Second Edition(8) Data CompressionThe information channels cost and transmission bottlenecks ma