Chapter 3 Baseband pusle and Digital Signaling
1 Chapter 3 Baseband Pusle and Digital Signaling
Chapter Obiectives Analog-to-digital signa ling(PCM and delta modulation) Binary and multilevel digitals signals Spectra and bandwidths of digital signals Prevention of intersymbol interference Time division multiplexing Packet transmission
2 Chapter Objectives • Analog-to-digital signaling(PCM and delta modulation) • Binary and multilevel digitals signals • Spectra and bandwidths of digital signals • Prevention of intersymbol interference • Time division multiplexing • Packet transmission
3.1 Introduction(main goals) To study how analog waveforms can be converted to digital waveforms. The most popular technique is called PCM To learn how to compute the spectrum for digital signals To examine how to filtering of pulse signals affects out a bility to recover the digital information at the receiver(isn To study how we can multiplex data from several digital bit streams into on high-speed digital stream fro transmission over a digital system. TDM)
3 3.1 Introduction(main goals) • To study how analog waveforms can be converted to digital waveforms. The most popular technique is called PCM • To learn how to compute the spectrum for digital signals • To examine how to filtering of pulse signals affects out ability to recover the digital information at the receiver(ISI) • To study how we can multiplex data from several digital bit streams into on high-speed digital stream fro transmission over a digital system.(TDM)
3.2 Pulse Amplitude Modulation PAM is an engineering term that is used to describe the conversion of the analog signal to a pulse-type signal in which the amplitude of the pulse denotes the analog information The sampling theorem gives a way to reproduce an analog waveform by using sample values of that waveform and sin(x)z orthogonal functions PAM Signaling is to provide another waveform that looks like pulses yet contains the information that was present in tha analog waveforn
4 3.2 Pulse Amplitude Modulation • PAM is an engineering term that is used to describe the conversion of the analog signal to a pulse-type signal in which the amplitude of the pulse denotes the analog information • The sampling theorem gives a way to reproduce an analog waveform by using sample values of that waveform and sin(x)/x orthogonal functions • PAM signaling is to provide another waveform that looks like pulses ,yet contains the information that was present in tha analog waveform
3.2 Pulse Amplitude Modulation The pulse rate, fs, for PAM is the same as that required by the sampling theorem, namely, f s >=2B, where b is the highest frequency in the analog waveform and 2B is called the nyquist rate Classification Nature sampling(gating) Instantaneous sampling(Flat-top type)
5 3.2 Pulse Amplitude Modulation • The pulse rate, fs , for PAM is the same as that required by the sampling theorem, namely, fs>=2B, where B is the highest frequency in the analog waveform and 2B is called the Nyquist rate. • Classification : Nature sampling(gating) Instantaneous sampling(Flat-top type)
3.2 Pulse Amplitude Modulation(Nature sampling or gating 显示该图片 Definition: if o(t) is an analog waveform bandlimited to B hertz, the PAM signal that uses natural sampling is o(t=o(ts(t) Where s(t) is a rectangular wave switching waveform and f=I/T>=2B s(t)=∑Ⅱ(t-k7,]/r) k=-oo ∑ k→)=∑Ⅱ(-k, k=-oo k
6 3.2 Pulse Amplitude Modulation(Nature sampling or gating) • Definition: if ω(t) is an analog waveform bandlimited to B hertz, the PAM signal that uses natural sampling is ωs (t)=ω(t)s(t) Where s(t) is a rectangular wave switching waveform and fs=1/Ts>=2B ( ) ∑∏ ) 1 ∑∏( ) ( s(t) ∑∏ [ - ]/ ∞ -∞ ∞ -∞ ∞ -∞ = = = = − = − = k k s k s d k T t k t t k T
3.2 Pulse Amplitude Modulation(PAM signal with natural sampling W(t) Ws(t) (a)Baseband Analog Waveform s(t) t (b)Switching waveform with Duty Cycle d=T/T=1/3 Figure 3-1 PAM Signal with natural sampling
7 3.2 Pulse Amplitude Modulation(PAM signal with natural sampling) (a) Baseband Analog Waveform S(t) t (b) Switching waveform with Duty Cycle d=τ /T =1/3 t W(t) W (t) s Figure 3-1 PAM Signal with natural sampling ≈ T τ
3.2 Pulse Amplitude Modulation( Generation of PAM with natural sampling) Analog bilateral switch Ws(t=W(t*s(t) s(o) clock Figure 3-2 Generation of PAM with natural sampling(gating) 8
8 3.2 Pulse Amplitude Modulation(Generation of PAM with natural sampling) clock S(f) Analog bilateral switch Ws(t)=w(t)*s(t) Figure 3-2 Generation of PAM with natural sampling (gating)
3.2 Pulse Amplitude Modulation(spectrum of a naturally sampled PAM) Theorem: the spectrum for a naturall sampled PAM signal is W()=Flo(O]=d 2 Sin na w(f-nys) =OO gn Where fs=1/Ts, Os=ifs, the duty cycle of s(t) is d=t/Ts and W(=Flo(t)I is the spectrum of the original unsampled waveform s()=(r-k7;1/r ∑Ⅱ(--k-)=∑∏(-kΣcnem0 k=-∞ k= 9
9 3.2 Pulse Amplitude Modulation(spectrum of a naturally sampled PAM) • Theorem: the spectrum for a naturally sampled PAM signal is : Where fs=1/Ts , ωs=2πfs , the duty cycle of s(t) is d=τ/Ts , and W(f)=F[ω(t)] is the spectrum of the original unsampled waveform. ∑ ∞ =-∞ ( - n ) πnd sin πnd ( ) = [ω ( )] = n s s s W f F t d W f f ( ) ∑∏ ∑∏ ∑ ∑∏ ∞ =-∞ ω ∞ =-∞ ∞ =-∞ ∞ =-∞ ) 1 - τ ) = ( τ - τ = ( s(t) = [ - ]/ τ k j n t n k k s k s s c e d k T t k t t k T ＝
3.2 Pulse Amplitude Modulation(spectrum of a naturally sampled PAM) wU) The spectrum of the PAM with natural sampling is a function of the spectrum of the analog input waveform The spectrum of the input analog waveform is repeated at harmonics of the sampling frequency wAn-2 l)w-d the PAM spectrum is zero for +3f, +6f and so on Because of d=1/3 and the spectrum in these harmonic bands is nulled out by the(sin(x)/x)function ( The bandwidth of the pam signal is smpingwitd= L3 and/=4B much larger than the bandwidth of Figure 33 Spectrum of a PAM waveform the original ananlog signal. the null bandwidth for the envelope of the Fig 3-3 Spectrum of a PAMPAM signalis 3f=12B, that is, the nt waveform with Natural bandwidth of this PAM signal is tell sampling(p132) times the bandwidth of the analog 10 Signa
10 3.2 Pulse Amplitude Modulation(spectrum of a naturally sampled PAM) • The spectrum of the PAM with natural sampling is a function of the spectrum of the analog input waveform • The spectrum of the input analog waveform is repeated at harmonics of the sampling frequency • the PAM spectrum is zero for ±3fs , ±6fs , and so on,Because of d=1/3, and the spectrum in these harmonic bands is nulled out by the (sin(x)/x) function • The bandwidth of the PAM signal is much larger than the bandwidth of the original ananlog signal. The null bandwidth for the envelope of the PAM signal is 3fs=12B, that is, the null bandwidth of this PAM signal is 12 times the bandwidth of the analog signal. • Fig. 3-3 Spectrum of a PAM waveform with Natural sampling(p132)
