Chapter 3: BASEBAND PULSE AND DIGITAL SIGNALING

1. Chapter 3:BASEBAND PULSE AND DIGITAL SIGNALING • 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 Eeng360 Communication Systems I Department of Electrical and Electronic Engineering Eastern Mediterranean University

2. INTRODUCTION • 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. • 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.

3. PULSE AMPLITUDE MODULATION • 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. • 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. • There are two classes of PAM signals: • PAM that uses Natural Sampling (gating); • PAM that uses Instantaneous Sampling to produce a flat-top pulse.

4. 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 andfs = 1/Ts ≥ 2B. 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, • cnrepresents the Fourier series coefficients of the switching waveform.

5. Natural Sampling (Gating) w(t) s(t) ws(t) =w(t)s(t)

6. Generating Natural Sampling • The PAM wave form with natural sampling can be generated using a CMOS circuit consisting of a clock and analog switch as shown.

7. Spectrum of Natural Sampling • The duty cycle of the switching waveform is d = τ/Ts = 1/3. • The sampling rate is fs = 4B.

8. Recovering Naturally Sampled PAM • 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 low-pass filter where the cutoff frequency is: B <fcutoff< fs -B • If the analog signal is under sampled fs < 2B, 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

9. Demodulation of PAM Signal • The analog waveform may be recovered from the PAM signal by using product detection,

10. Instantaneous Sampling (Flat-Top PAM) • This type of PAM signal consists of instantaneous samples. • w(t) is sampled at t = kTs . • The sample values w(kTs ) determine the amplitude of the flat-top rectangular pulses.

11. Instantaneous Sampling (Flat-Top PAM) • 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:

12. The spectrum of the flat-top PAM • Analog signal maybe recovered from the flat-top PAM signal by the use of a LPF. 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).

13. 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 • 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.