3.2 Pulse Amplitude Modulation(receiver) Low-pass filter W(s) PAM Analog Multiplier (natural ffour-quadrants multiplier B<f cutoff f-B sampling f>=2B Low Pass Cwif) If the analog Filter H(f gnal IS under sampled (f 2B), Oscillator fco fco Wo=nws pectral overlapping B〈fco〈fs-B Fig 3-4 Demodulation (aliasing) is raised. of a pam signal Product detection noise due to power supply hum or noise due to mechanical circuit vibration might fall in the band corresponding to low frequency band and other bands might be relatively noise free
11 3.2 Pulse Amplitude Modulation(receiver) • Fig.3-4 Demodulation of a PAM signal • Low-pass filter B<fcutoff<fs -B fs>=2B If the analog signal is under sampled(fs<2B), spectral overlapping (aliasing) is raised. • Product detection noise due to power supply hum or noise due to mechanical circuit vibration might fall in the band corresponding to low frequency band and other bands might be relatively noise free Low Pass Filter H(f) Oscillator Wo=nws -fco fco f H(f) B〈fco〈fs-B Analog Multiplier (four-quadrants multiplier) W(s) PAM (natural sampling Cw(f)
3.2 Pulse Amplitude Modulation( instantaneous sampled or Flat-top PAM) 无法显示该图片 Definition: if o(t)is an analog waveform bandlimited to B hertz, the PAM signal that uses natural sampling is (t)= 2o(kTs h(t-kTs) Where h(t denotes the sampling-pulse shape and, for flat-top sampling the pulse shape is h(t)=II(t/xFlforltk t2, andO)t(>2 Where t<t=f and[s=2B
12 3.2 Pulse Amplitude Modulation( instantaneous sampled or Flat-top PAM) • Definition: if ω(t) is an analog waveform bandlimited to B hertz, the PAM signal that uses natural sampling is Where h(t) denotes the sampling-pulse shape and , for flat-top sampling, the pulse shape is: Where τ<=Ts=1/fs and fs>=2B ∑ ∞ =-∞ s s s ω (t) = ω(kT )h(t - kT ) k h(t) =∏(t / )＝1 for | t |/2, and 0| t |/2
3.2 Pulse Amplitude Modulation Ws(t) PAM with flat-top sampling is called instantaneous 0 samples, since o(t)is sampled at t=kTs and .(a Baseband Analog waveform samplevalue o(kT determine the amplitude of the flat-top rectangular uIse (b)Impulse Train Sampling waveform. The flat-top signal could be Ws(t) generated by using a sample-and-hold type of electronic circuit Note that if h(t=sinx/x with overlapping pulses, then becomes identical to the c)Resulting PAM Signal sampling theorem flat-top sampling, d=T/Ts=1/3) ig 3-5 PAM Signal with flat-top O、()=>o(kIh(-kT 13 sampling
13 3.2 Pulse Amplitude Modulation • Fig 3-5 PAM signal with flat-top sampling ∑ ∞ =-∞ s s s ω (t) = ω(kT )h(t - kT ) k • PAM with flat-top sampling is called instantaneous samples, since ω(t) is sampled at t=kTs and sample value ω(kTs ) determine the amplitude of the flat-top rectangular pulse • The flat-top signal could be generated by using a sample-and-hold type of electronic circuit • Note that if h(t)=sinx/x with overlapping pulses, then becomes identical to the sampling theorem t Ws(t) 0 (a) Baseband Analog waveform t (b) Impulse Train Sampling waveform τ →Ts← Ws(t) t (c) Resulting PAM Signal ( flat-top sampling , d=τ/Ts=1/3 )
3.2 Pulse Amplitude Modulation--the spectrum of flat-top PAM signal Theorem: the spectrum for a flat-top PAM signal Is. W()(I/T)H()2w(-kfs) where HO=F(h(o)=r(sInrtf Proof: o、()=20(kTsh(t-kTs) k
14 3.2 Pulse Amplitude Modulation—the spectrum of flat-top PAM signal • Theorem: the spectrum for a flat-top PAM signal is: where Proof: ∑ ∞ =-∞ ( ) = (1/ ) ( ) ( - k ) n s s s W f T H f W f f ) sin ( ) ( ( )) ( f f H f h t ＝F = ∑ ∞ =-∞ s s s ω (t) = ω(kT )h(t - kT ) k
3.2 Pulse Amplitude Modulation--the spectrum of flat-top PAM signal IWO) B (a) Magnitude Spectrum of Input Analog Waveform Iw,Of) H))∑w(f-k, )-÷|=m21 3f. (b)Magnitude Spectrum of PAM(flat-top sampling), T/T, 1/3 ands =4B Figure 3-6 Spectrum of a PAM waveform with flat-top sampling 5
15 3.2 Pulse Amplitude Modulation—the spectrum of flat-top PAM signal