short review HDB3 B8ZS rect pulses consider pulse of width tau p(t) = Arect(t/tau) -> fourier -> Atau*sinc(f/tau) cutoff freq percent power 1/tau 90% 1.5/tau 93% 2/tau 95% 3/tau 96.5% 4/tau 97.5% 5/tau 98% optimum pulse width is Tb (bit period) if tau > Tb, pulses overlap (bad) if tau < Tb, BW wasted if source sends data at rate of Rb bps, Tb = 1/Rb and optimum tau = 1/Rb need good pulse shape want smooth shape for bandwidth min must make sure pulse transmitted to rep a particular bit does not interfere at receiver with pulse transmitted at next bit, ISI is bad sinc shaped pulses transmit data at a higher rate for the same bw with greater accuracy than rect pulses noise margin is the dist between a noiseless received sig and the thresh at the instant of sampling timing jitter reduces the noise margin for sinc signals rect can be off a ton and still have a good noise margin ex7-3: need 100% accuracy (no pulse distortion) over an ideal baseband channel how much bw is needed for a data rate of 10Kbps = Rb BWmin = 10KHz/2 = 5Khz missed some stuff... BWmin = Rb/2 = 25Khz Tb=1/Rb = 20us should sample in middle of bit time, 10us, 30us, 50us, 70us, 90us p = sum(pi(t)) p1(t) = sinc(pi*(t-10us)/20us) p2(t) = sinc(pi*(t-30us)/20us) suppose receiver is not perfectly synchronized if sampled at 50us, p(t) = -1 drops off quickly or not at all depending on shift could also used raised cosine, flatter tails to reduce ISI p = Asinc(tpi*Rb)*cos(2tpi*fx)/(1-16ttfxfx) fx is excess bandwidth pulse freq response: P = {A/Rb on abs(f) <= a, A/2Rb * (1-sin(pi/2fx * ...)) on a<=abs(f)<=b, 0 on abs(f)>b} larger values of fx require larger bw but also provide more damping thus a narrower main lobe and flatter tails, will reduce ISI define rolloff factor r as 2fx/Rb, r between 0 and 1 raised cosine: r=0.5 -> B = Rb/2 * (1+r) = 37.5KHz pulses don't drop off as fast as cosine duobinary signaling in 1963 adam lender showed it was possible to xmit Rb bps with no ISI using theoretical min bw of Rb/2 Hz w/o using ideal filters technique is called duobinary sig or correlative coding or partial response sig basic idea is to introduce some controlled ISI into data stream instead of trying to eliminate it completely input put through mapping to get data bits (+/-1), combine delayed data bits with original stream of data bits, lob into the channel ex: xk 0 0 1 0 1 1 0 ak -1 -1 1 -1 1 1 -1 bk -2 0 0 0 2 0 decoding rule: if yk = 2, xk = 1 if yk = -1, xk = -1 if yk = 0, xk = 0-xv(k-1) what if receive 2 0 0 0 2 0 decode 1 -1 1 -1 1 -1