1、Last ContentsChapter 1 Random Process 1.11 Representation of Narrowband Noise in Terms of In-phase and Quadrature Components1.12 Representation of Narrowband Noise in Terms of Envelope and Phase Components 1.13 Sine Wave Plus Narrowband NoiseChapter 2 Continuous-Wave Modulation2.1 Introduction2.2 Am

2、plitude Modulation2.3 Linear Modulation Schemes1Outline-1Representation of narrowband noise The canonical form (Equ. 1.100) Properties of the in-phase and quadrature components (p. 65-66) Representation using envelop and phase components (Equ. 1.105-1.107) Basic concepts of Rayleigh distribution and

3、 Rician distribution 2Outline-2AM AM signal (Equ. 2.2 and Fig. 2.3), and the amplitude sensitivity ka Conditions of correct detection (p. 90) Spectrum of AM wave (Equ. 2.5 and Fig. 2.4) Transmission bandwidth BT = 2W Virtues and limitations of AM 3Outline-3Linear modulation schemes The general form

4、(Equ. 2.7) DSB DSB signal (Equ. 2.8 and Fig. 2.5) Spectrum of DSB wave (Equ. 2.9 and Fig. 2.6) Coherent receiver Basic knowledge of costas receiver Basic concept of quadrature-carrier multiplexing 4Representation of narrowband noise in terms of in-phase and quadrature componentRepresentation in term

5、s of in-phase and quadrature component(1.100)(1.108)5Representation of narrowband noise in terms of Envelope and Phase ComponentsRepresentation of Narrowband Noise in terms of Envelope and Phase Components(1.105)(Reyleigh distribution)6Properties of narrowband noiseThe in-phase and quadrature compon

6、ent of narrowband noise have zero mean.If the narrowband noise is Gaussian, the in-phase and quadrature components are jointly Gaussian.If the narrowband noise is stationary, then its in-phase and quadrature components are jointly stationary7Properties of narrowband noiseThe in-phase and quadrature

7、component of narrowband noise have the same variance as the narrowband noise n(t).Both in-phase and quadrature components have the same power spectral density related to spectral density of the narrow-band noise8Properties of narrowband noiseThe cross-spectral density of the in-phase and quadrature

8、components of narrowband noise is purely imaginary, as.If the narrowband noise is Gaussian and its power spectral density is symmetric about the mid-band frequency fc, then the in-phase component and quadrature component are statistically independent(1.102)9Sine Wave Plus Narrowband NoiseMixture of

9、sine wave and narrowband noise(1.119)(1.120)(1.121)We assume n(t) is Gaussian with zero mean and variance 2.Both nI(t) and nQ(t) are Gaussian and statistically independentThe mean of nI(t) is A and that of nQ(t) is zero.The variance of both nI(t) and nQ(t) is 2.101.13 Sine Wave Plus Narrowband Noise

10、Figure 1.23 Normalized Rician distribution.112.1 IntroductionContinuous-wave modulationAmplitude modulationthe amplitude of the sinusoidal carrier wave is varied in accordance with the baseband signalAM, DSB,VSB,SSBLinear modulationAngle modulationthe angle of the sinusoidal carrier wave is varied i

11、n accordance with the baseband signalFM,PM12 Figure 2.3 Illustrating the amplitude modulation process|Kam(t)|1Amplitude ModulationEnvelop detectionOvermodulated13Fourier transform of the AM waveFigure 2.4 (a) Spectrum of baseband signal (b) spectrum of AM wave142.3 Linear Modulation Schemesh(t)m(t)s

12、m(t)cos(2fct)General mode of linear Modulation152.3 Linear Modulation SchemesDouble sideband-suppressed carrier (DSB-SC) modulationEnvelop detector cannot be usedCoherent detection is requiredThe frequency of the local oscillator is adjusted to be the same as the carrier frequencyPhase controllerPLL

13、162.3 Linear Modulation Schemes172.3 Linear Modulation SchemesCoherent detection(2. 10)Figure 2.7 Coherent detector for demodulating DSB-SC modulated wave18This Contents2.3 Linear Modulation Schemes 2.4 Frequency Translation2.5 Frequency-Division Multiplexing2.6 Angle Modulation2.7 Frequency Modulat

14、ion19Single-sideband modulation (SSB)Single-sideband modulation (SSB)Only upper or lower sideband is transmittedby frequency discrimination method.The message spectrum must have energy gap centered at the origin. (Eg., voice signal)20Single-sideband modulation (SSB)21原理兩個邊帶包含相同的信息只需傳輸一個邊帶：上邊帶或下邊帶要求m

15、(t)中無太低頻率方法濾波法相移法-f0HL(f)特性上邊帶(b) 上邊帶濾波器特性和信號頻譜f00f單邊帶信號的頻譜上邊帶S(f)上邊帶下邊帶HH(f)特性HH(f)特性(a) 濾波前信號頻譜(c) 下邊帶濾波器特性和信號頻譜S(f)S(f)-f00f-f0f0f下邊帶f0上邊帶22Single-sideband modulation (SSB)HSSB(f)m(t)c(t)SDSB(t)SSSB(t)23濾波法的技術難點濾波特性很難做到具有陡峭的截止特性需要過渡頻段可以采用多級（一般采用兩級）DSB調制及邊帶濾波的方法，即先在較低的載頻上進行DSB調制，目的是增大過渡帶的歸一化值，以利于濾

16、波器的制作。再在要求的載頻上進行第二次調制當調制信號中含有直流及低頻分量時濾波法就不適用了。24相移法和SSB信號的時域表示Single-sideband modulationCan be derived by Hilbert transformHilbert transform = 90-degree phase shift.90 degree phase shift regardless of frequency.25相移法和SSB信號的時域表示SSB信號的時域表示式兩式僅正負號不同26相移法和SSB信號的時域表示“”表示上邊帶信號，“+”表示下邊帶信號希爾伯特變換：上式中Am sinmt

17、 可以看作是Am cosmt 相移/2的結果。把這一相移過程稱為希爾伯特變換，記為“ ”，則有27相移法和SSB信號的時域表示一般情況下：-jsgn可以看作是希爾伯特濾波器傳遞函數，即28移相法SSB調制器方框圖優點：不需要濾波器具有陡峭的截止特性。缺點：寬帶相移網絡難用硬件實現。Hilbert transform = 90-degree phase shift.29Receiver for SSBCoherent detectionCan use pilot signal for demodulationPhase distortion30SSB信號的性能SSB信號的實現比AM、DSB要復雜

18、SSB調制方式在傳輸信息時，不僅可節省發射功率，而且它所占用的頻帶寬度比AM、DSB減少了一半。它目前已成為短波通信中一種重要的調制方式。31Vestigial sideband (VSB) modulation原理：殘留邊帶調制是介于SSB與DSB之間的一種折中方式。克服了DSB信號占用頻帶寬的缺點，又解決了SSB信號實現中的困難。在這種調制方式中，不像SSB那樣完全抑制DSB信號的一個邊帶，而是逐漸切割，使其殘留小部分，如下圖所示：32Vestigial sideband (VSB) modulation特點適合包含直流分量和很低頻率分量的基帶信號。原理VSB仍為線性調制濾波器的特性應按殘

19、留邊帶調制的要求來進行設計。33Vestigial sideband (VSB) modulationFigure 2.12 Filtering scheme for the generation of VSB modulated wave.Vestigial sideband (VSB) modulation34Vestigial sideband (VSB) modulationr(t)接收信號m(t)cos0tH1(f)基帶信號m(t)解調接收機r(t)的頻譜：濾波輸出信號的頻譜：35Vestigial sideband (VSB) modulation為了無失真地傳輸，要求由于所以，上

20、式可以寫為上式即產生VSB信號的條件。36Vestigial sideband (VSB) modulation37Vestigial sideband (VSB) modulationVSB|H(fc)| = 1/2The sum of the values of the magnitude response |H(f)| at any two frequencies equally displaced above and below fc is unity. the phase reponse arg(H(f) is linear Figure 2.13 Magnitude respons

21、e of VSB filter ;only the positive-frequency portion is shown.38Vestigial sideband (VSB) modulationVestigial sideband (VSB) modulationNon-linear AM (carrier included)Non-coherent detection (envelop detection : diode, RC)Low costLinear modulation (DBS-SC, SSB)Carrier (pilot signal (not carrier) can b

22、e sent separately)Coherent detection neededHigh costSSB with carrierDetection by envelope detector.Ideal filter or gap in the energy.39Carrier included envelop detection40Carrier included envelop detection41Television signalsFigure 2.15 (a)Idealized magnitude spectrum of a transmitted TV signal.(b)M

23、agnitude response of VSB shaping filter in the receiver.42Television signalsTelevision signals432.4 Frequency TranslationFigure 2.16 Block diagram of mixer.442.4 Frequency TranslationFigure 2.17 (a) Spectrum of modulated signal s1(t) at the mixer input. (b) Spectrum of the corresponding signal s(t)

24、at the output of the product modulator in the mixer.Up conversion:Down conversion:45CH2CH1CH3原帶寬CH1CH2CH3移頻后帶寬MUXCH1CH2CH3帶寬復用f適用于模擬信號傳輸 2.5 Frequency Division MultiplexingFDM462.5 Frequency Division MultiplexingFigure 2.18 Block diagram of FDM system.472.5 Frequency Division MultiplexingFigure 2.19

25、 Illustrating the modulation steps in an FDM system482.5 Frequency Division Multiplexing492.6 Angle ModulationAngle Modulation Non linear modulationFM & PMThe amplitude of the carrier wave is maintained constant.can provide better discrimination against noise and interference than amplitude modulati

26、onThe improvement in performance is achieved at the expense of increased transmission bandwidthSuch a trade-off is not possible with AM, regardless of its form. 50 Basic Definitions: 2.6 Angle Modulationinstantaneous angle of a modulated sinusoidal carrier .instantaneous phase deviation.carrier ampl

27、itudeinstantaneous frequencyinstantaneous frequency deviation.51 Phase modulation (PM)2.6 Angle Modulationphase sensitivity522.6 Angle ModulationFrequency modulation (FM)Frequency sensitivity532.6 Angle ModulationFM PMFrequency modulationFrequencymodulatorPhasemodulatorPhase modulation542.6 Angle Mo

28、dulationFM PMFigure 2.20 Illustrating the relationship between frequency modulation and phase modulation. (a) Scheme for generating an FM wave by using a phase modulator. (b) Scheme for generating a PM wave by using a frequency modulator.552.7 Frequency ModulationFM is nonlinearNarrowband FM (NBFB)W

29、ideband FM (WBFB)56Narrowband FM (NBFB)Signal-tone NBFM(2.27)(2.28)(2.30)frequency deviationmodulation index57Narrowband FM (NBFB)Modulation index of FM(2.33)(2.32)Narrow band FM : is small compared to one radianWideband FM : is large compared to one radian58Narrowband frequency modulation59Narrowba

30、nd frequency modulation60Amplitudeof NBFM & AMAmplitudeNBFMNBFM has varying amplitude61Amplitudeof NBFM & AM AMs variation is largerAM62Spectrum of NBFM & AMAlternative analysis63Spectrum of NBFM642.7 Frequency ModulationFigure 2.22A phasor comparison of narrowband FM and AM waves for sinusoidal mod

31、ulation. (a) Narrowband FM wave. (b) AM wave.65Demodulation of NBFMCoherent detection 66Wideband frequency modulation(WBFB)(2.33)67Wideband frequency modulation(WBFB)N-th order Bessel function of the first kind68Wideband frequency modulation(WBFB)(2.48)(2.49)69Bessel functionBessel function For smal

32、l Figure 2.23 Plots of Bessel functions of the first kind for varying order.70Properties of WBFMSpectrum of FM signal contains a carrier and an infinite set of side frequenciesTransmission BW is very wideSmall (narrowband FM): only J0() and J1() are not negligibleBW : similar to AMAverage Power of F

33、M is a constantPower of carrier: determined by J0() unlike AM.Total power(2.54)712.7 Frequency ModulationExample 2.2 Fixed freq., varying amplitudeFixed amplitude, varying frequency722.7 Frequency ModulationTransmission bandwidth of FM signalsTheoretically, infiniteEffectively limited to a finite nu

34、mber of significant side frequencies.According to previous figure, the components outside f decreases rapidlyCarsons rule :(2.55)732.7 Frequency ModulationAlternative assessment of BW requirementMax n that satisfies |Jn()| 0.01742.7 Frequency ModulationConsider the more general case of an arbitrary

35、modulating signal m(t) which highest frequency component denoted by W,then the actual bandwidth of FM is larger than Carsons rules value, but smaller than the value shown in Figure 2.26 .Carsons rule752.7 Frequency ModulationExample 2.3In North America FM radio, f = 75 kHz, W = 15 kHzBy Carsons rule

36、 From table ( = 75/15 = 5)BTG=16 * 15 = 240 kHz (From the fig., 3.2*75 = 240)Measured BW is 200kHzCarsons rule underestimates the transmission bandwidth by 10 percent, whereas the universal curve in Fig. 2.26 overestimates it by 20 percent76NFMFigure 2.27 Block diagram of the indirect method of gene

37、rating a wideband FM signal.Generation of FM signalsDirect FMCarrier frequency is directly varied by voltage controlled oscillator.Indirect FMGenerate narrow-band FM (by phase modulation) followed by frequency multiplicationPreferred choice when the carrier frequency is of major concern as in commer

38、cial radio broadcasting.77Figure 2.28 Block diagram of frequency multiplierFrequency multiplierReason for starting with narrow band FM for frequency stability.Use N-th harmonics Apply band pass filter around nfc78Frequency multiplierEx.modulation indexmodulation index79Demodulation of FM SignalsDire

39、ct method: Frequency discriminatorThe instantaneous output amplitude of the frequency discriminator is directly proportional to the instantaneous frequency of the input FM signal.Slope circuit followed by envelope detectorIndirect method: Phase-locked loop802.7 Frequency ModulationFigure 2.29 (a) Frequency response of ideal slope circuit. (b) Frequency response of the slope circuits complex low-pass equivalent. (c) Frequency response of the idea