Chapter 3 BASEBAND PULSE AND DIGITAL SIGNALING Chapter
Chapter 3: BASEBAND PULSE AND DIGITAL SIGNALING Ø Chapter Objectives: • Analog-to-digital signaling (pulse code modulation ) Binary and multilevel digitals signals • Spectra and bandwidths of digital signals • Prevention of intersymbol interference • Time division multiplexing • Packet transmission Huseyin Bilgekul Eeng 360 Communication Systems I Department of Electrical and Electronic Engineering Eastern Mediterranean University Eeng 360 1
INTRODUCTION Ø This chapter we study how to encode analog waveforms into base band digital signals. Digital signal is popular because of the low cost and flexibility. Ø Main goals: • To study how analog waveforms can be converted to digital waveforms, Pulse Code Modulation. • To learn how to compute the spectrum for digital signals. • Examine how the filtering of pulse signals affects our ability to recover the digital information. Intersymbol interference (ISI). • To study how we can multiplex (combine) data from several digital bit streams into one high-speed digital stream for transmission over a digital system Time-division Multiplexing. Eeng 360 2
PULSE AMPLITUDE MODULATION Ø Pulse Amplitude Modulation (PAM) 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. Ø The purpose of PAM signaling is to provide another waveform that looks like pulses, yet contains the information that was present in the analog waveform. Ø There are two classes of PAM signals: • PAM that uses Natural Sampling (gating); • PAM that uses Instantaneous Sampling to produce a flat-top pulse. Eeng 360 3
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Natural Sampling (Gating) DEFINTION: If w(t) is an analog waveform bandlimited to B hertz, the PAM signal that uses natural sampling (gating) is ws(t) =w(t)s(t) Where S(t) is a rectangular wave switching waveform and fs = 1/Ts ≥ 2 B. THEORM: The spectrum for a naturally sampled PAM signal is: • Where fs= 1/Ts, ωs = 2π fs, • the Duty Cycle of s(t) is d = τ/Ts , • W(f)= F[w(t)] is the spectrum of the original unsampled waveform, • cn represents the Fourier series coefficients of the switching waveform. Eeng 360 5
Natural Sampling (Gating) w(t) s(t) ws(t) =w(t)s(t) Eeng 360 6
Spectrum of Natural Sampling Assuming that W(f) is as shown • The duty cycle of the switching waveform is d = τ/Ts = 1/3. • The sampling rate is fs = 4 B. Eeng 360 7
Recovering Naturally Sampled PAM Ø At the receiver, the original analog waveform, w(t), can be recovered from the PAM signal, ws(t), by passing the PAM signal through a lowpass filter where the cutoff frequency is: B <fcutoff < fs -B Ø If the analog signal is under sampled fs < 2 B, the effect of spectral overlapping is called Aliasing. This results in a recovered analog signal that is distorted compared to the original waveform. LPF Filter B <fcutoff < fs -B Eeng 360 8
Demodulation of PAM Signal Ø The analog waveform may be recovered from the PAM signal by using product detection, Eeng 360 9
Instantaneous Sampling (Flat-Top PAM) • This type of PAM signal consists of instantaneous samples. • w(t) is sampled at t = k. Ts. • The sample values w(k. Ts ) determine the amplitude of the flat-top rectangular pulses. Eeng 360 10
Instantaneous Sampling (Flat-Top PAM) Ø DEFINITION: If w(t) is an analog waveform bandlimited to B Hertz, the instantaneous sampled PAM signal is given by – Where h(t) denotes the sampling-pulse shape and, for flat-top sampling, the pulse shape is, THEOREM: The spectrum for a flat-top PAM signal is: Eeng 360 11
The spectrum of the flat-top PAM Ø Analog signal maybe recovered from the flat-top PAM signal by the use of a LPF Response Note that the recovered signal has some distortions due to the curvature of the H(f). Distortions can be removed by using a LPF having a response 1/H(f). Eeng 360 12
Some notes on PAM • The flat-top PAM signal could be generated by using a sample-and -hold type electronic circuit. • There is some high frequency loss in the recovered analog waveform due to filtering effect H(f) caused by the flat top pulse shape. • This can be compensated (Equalized) at the receiver by making the transfer function of the LPF to 1/H(f) • This is a very common practice called “EQUALIZATION” • The pulse width τ is called the APERTURE since τ/Ts determines the gain of the recovered analog signal Ø Disadvantages of PAM • PAM requires a very larger bandwidth than that of the original signal; • The noise performance of the PAM system is not satisfying. Eeng 360 13
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