Lecture2-SignalsAndSignalAnalysis

1、Data Communications and Networking數(shù)據(jù)通信與計算機網(wǎng)絡數(shù)據(jù)通信與計算機網(wǎng)絡授課教師：授課教師： 劉振盛劉振盛武漢大學武漢大學 電氣工程學院電氣工程學院School of Electrical Engineering, Wuhan University.By Liu ZhenshengEmail: Lecture 2. 2.5 Noise2.4 Periodic and Aperiodic Signals2.3 Analog and Digital Signals2.2 Time-domain and Frequency-domain Analysis2.1 I

2、nformation and SignalsLecture 2. Data communications and networking2.1 Information and Signals Information reduction of uncertainty, that is , reduction of entropy（熵熵）Assume： probability of a message is p, then Information Capacity of the message is I = log 2 1/p （bit） Signals representation form of

3、 information In data communication, signals are electromagnetic signals or optical signals corresponding with the data generally. To be transmitted, information must be transformed into signals.Signals must match with the transmission medium.Data communications and networking Type of Signals Continu

4、ous and discrete signals Continuous signals- continuous ,it can be all possible values and be called analog signals. Discrete signals-discrete and discontinuous impulses, and it be called digital signals. Random and certain signals All signals are random signals except regular signals that are produ

5、ced in lab. Only random signals include information. Periodic and aperiodic signals Periodic signals are certain signals and have no information. Data communications and networking2.2 Time-domain and Frequency-domain Analysis 2 analysis methods for continuous signals: Time-domain analysis and Freque

6、ncy domain analysis.A. Time-domain analysis（時域分析）：（時域分析）： Basic theory: Adscititious complicated impulses (input signals) can be decomposed into a series of unit impulses in time domain. We can compute impulse response for each unit impulse. All impulse responses be superposed (迭加迭加) to the total re

7、sponse (output signals). Mathematical tool: integral transform, convolution（卷積）（卷積） r(t) = e(t)h(t) e(t)-impulse function h(t)-impulse response function Representation: time-domain plot 圖圖 (waveform plot ) Time-domain plot shows changing of signal amplitude with time. Data communications and network

8、ingAny composite signal can be represented as a sum of simple sine wavesTime-domain analysisData communications and networkingB. Frequency-domain analysis (頻域分析頻域分析): Basic theory: Any signals can be decomposed into a lot of sine waves withdifferent frequency, amplitude and phase. Periodic signal is

9、 made of discrete frequency components (fundamental frequency and harmonics). Aperiodic signal can be seen as periodic signal whose periodis infinite( ). Mathematical tool: Fourier transform（傅立葉變換傅立葉變換）dtetfjwFdwejwFtfjwtjwt)()()(21)(f(t)-original functionF(jw)-frequency spectrum function Representa

10、tion: frequency-domain plot or spectrum plot(including amplitude-frequency plot and phase-frequency plot) It is used to show the characteristic of amplitude and phase of signal with different frequency.Data communications and networkingExample for frequency-spectrum plot Example 1: Frequency-spectru

11、m plot for single frequency signal Data communications and networking Example 2: Time-domain plot for harmonic frequency signalsData communications and networkingFrequency-spectrum plot for signal with the fundamental , 3rd and 5th harmonic frequency signalsTime-domainFrequency-spectrumData communic

12、ations and networking Example 3: Frequency-spectrum plot for rectangular (矩形矩形) single impulseData communications and networkingImportant conclusion: Periodic signal has discrete frequency-spectrum. Single impulse has continuous frequency-spectrum and its Significant bandwidth (有效帶寬有效帶寬) is 1 / Data

13、 communications and networking2.3 Analog and DigitalA、Analog Signals Simple Analog Signals Sine wave is the most fundamental analog signal. It cannot be decomposed. Sine wave can be fully described by three characteristics : Amplitude Frequency (period) PhaseMore about frequency: If a signal does no

14、t change at all, its frequency is 0 Hz. (DC) If a signal changes instantaneously, its frequency is infinity and period is 0; since frequency is the inverse of period. More about phase: Phase describes the relative position to time zero of the waveform.Data communications and networking Composite Sig

15、nals No matter how complex, any periodic signals can be decomposed into a collection of sine waves after Fourier Analysis, each having a measurable amplitude, frequency, and phase. Example: a signal with/without a DC componentData communications and networking bandwidth is width of frequency spectru

16、m of a signal Bandwidth Important property of a medium Difference between highest and lowest frequency that can pass through the medium Measured in Hertz Hz Limits the channels capacityData communications and networking Data can be represented by some digital impulse. Waveform parameter:Bit period:

17、the time required to send one single bit.Bit rate: the number of bit periods per second, bps or b/s. Frequency-domain analysis: A digital signal can be decomposed into an infinite number of simple sine waves called harmonics, each with a different amplitude, frequency and phase.B、Digital SignalsData

18、 communications and networking Transmission of digital signals: To receive an exact replica (復制品復制品) of the digital signal, all of frequency components must be faithfully transferred through transmission medium. If some of many components are not passed through the medium,Distortion (畸變畸變) of the si

19、gnal is engendered at the receiver. Data communications and networking Significant bandwidth (half power bandwidth) 有效帶寬有效帶寬 半功率帶寬半功率帶寬 If we send only those components whose amplitudes are significant and whose power is a half of power of whole signals, we can still recreate the digital signal with

20、 reasonable accuracy (minimum Distortion,最小畸變最小畸變) at the Receiver. we call this part of spectrum significant bandwidth . Exact and Significant Spectrums Data communications and networking Analog signals may be periodic or aperiodic , and digital one also.l A aperiodic signal can be decomposed into

21、infinitenumber of periodic signals.l In communication systems, actual signal are aperiodic signals.l A aperiodic signal can be seen as a periodic signal withinfinite period ( ) 2.4 Periodic and Aperiodic SignalsData communications and networking2.5 Noise n Noises are bad signals brought by many fact

22、or in communication system. n Noises can change or even break information (interfere).n If the signal distortion is serious,the receiver cannot return to the original signal. Data communications and networking Thermal Noisel It is produced by Brown movement of electriferous particle in any circuit o

23、r system working up 0 K.l It is called Gaussian noise (高斯噪聲高斯噪聲) or white noise (白噪聲白噪聲)because its power spectrum is gaussian distribution.l Thermal noise is inescapable(不可避免的不可避免的).Thermal Noise InterModulation Noise Crosstalk Impulse 熱噪聲熱噪聲 交調(diào)噪聲交調(diào)噪聲 串音串音 脈沖噪聲脈沖噪聲 Types of noisesData communication

24、s and networking InterModulation Noisel Many additional frequencies are produced such as frequency sum or difference and so on which interfere original signals when many different signals are transmitted in the same medium.l Some nonlinearity in receiver ,sender and transmission system produce new f

25、requency too.l Intermodulation noise can be controlled or improved by revise of the system. Crosstalk l One signal enters into a adjacent channel to create interfere for bad coupling(耦合耦合) inter-channels. It is also called adjacent channel interfere (鄰道干擾鄰道干擾). l It is presence in multiplex system.D

26、ata communications and networking Impulse Noisel Natural and artificial electromagnetic noises couple into the channel.l For example , thunder, electrical arc while power switch is working, automobile portfire.l Although duration of emergent impulse noise is short, it may have very strong power.l Im

27、pulse noise is main reason for error in data communication.Data communications and networkingMeasurement of noise Ratio of signal to noise (SNR) (信噪比信噪比) Jamming of noise to signal does not depend on the Amplitude of noise but relative value of the signal power to the noise power.Undesired signal ad

28、ded to the transmitted signal Thermal noise Random motion of electrons Independent of frequency (”white noise”) and amplitude Added to the signalSignal-to-noise ratio, SNRS/N, where S is signal power, N is noise powerData communications and networkingSNR - ratio of average power of signal to that of noiseSNR = 10log10S/N (dB)n The bigger