several types of NRZ
	L: bits represented by voltage levels
	M: mark (binary one) represented by a state transition, spaces cause no change
	S: space (binary zero) represented by a state transition, marks cause no change

unipolar RZ: one rep by half-bit wide pulse, zero by no pulse
bipolar RZ: ones and zeros are repped by opposite level pulses that are half-bit wide
RZ AMI: alternate mark inversion - ones repped by equal amp alternating pulses, zeros by nothing, talked about B8ZS without saying it
bi phase
	L: ones are a downward transition, zeros are upward transition
	M: midbit transitions are ones, no transition is a zero
	S: midbit transitions are zeros, no transition is a one

delay modulation aka miller coding: ones are repped by a midbit xition...
dicode NRZ: bit changes signified by a change in polarity, mid level means no change from previous bit
dicode RZ: dicode NRZ with halfbit pulses

transmitted waveform is a random process since actual data is random
to calc power spectral density, use wiener-khintchine theorem or a less rigorous approach (valid as long as each bit has the same prob and bits are indep)
let the transmitted sig be a sequence of pulses: y = sum<k=1,N>(akp(t-kTb))
where amplitudes (ak) of the pulses convey the info and the pulse p is arbitrary but time limited to Tb

energy spectral density: PSIy = PSIx*mag(P(f))^2
p is the transfer function
PSD = ESD/time to transmit data stream = Sy = PSIy/NTb = mag(Y)^2 * 1/NTb
Y = F{y(t)} = F{sum<k=1,N>(akp(t-kTb))} = sum<k=1,N>(akF{p(t-kTb)}) = sum<k=1,N>(akPe^(-jfk2pi*Tb)) -> X = sum<k=1,N>(ake^(-jfk2pi*Tb))

Sy = (PSIx * mag(P)^2)/NTb
PSIx = mag(X)^2 = X * X* = (sum<k=1,N>(ake^(-jfk2pi*Tb)))(sum<k=1,N>(ake^(jfk2pi*Tb))) = sum<k=1,N;m=1,N>(akame^(jf2pi*Tb*(k-m)))
the final equation here yields crazy for increasing N
let R0 = lim<N,inf>(1/N * sum<k=1,N>(akak))
let Rn = lim<N,inf>(1/N * sum<k=1,N>(akav(k+n)))
turns out this is a discrete autocorrelation
Sy = mag(P)^2 * 1/Tb * (R0+2sum<n=1,N>(Rncos(n2fpi*Tb))) = mag(P)^2 * 1/Tb * sum<n=inf>(Rncos(2nfpi*Tb))

some examples: polar signaling
1->+p
0->-p
ak is +/-1 with equal prob
R0 = lim<N,inf>(1/N * sum<k=1,N>(akak)) = 1
R1 = lim<N,inf>(1/N * sum<k=1,N>(akav(k+1))) = equally likely to be +/-1, time averaging = 0 (ditto for all other Rn)

using half-width rects (bipolar RZ)
p is a rect, P = Tb/2 * sinc(fpi/2 * Tb)
Sy = Tb/4 * sinc^2(fpi/2 * Tb)
essential bandwidth in 2/Tb

on-off sig (unipolar RZ)
1 is pulse
0 is no pulse
ak = 0 or 1, equal prob
R0 = 1/N * sum<k=>(akak), consider as avg value, 0 or 1, 0.5 is expected
Rn = 1/N * sum<k=>(akav(k+n)), consider as avg value, only opts are 0 and 1, will be 0 3/4 of the time, 1 1/4 of the time, expected value is 0.25
Sy = mag^2(P)/Tb * (R0+2sum<n=1,inf>(Rncos(2nfpi*Tb))) = mag^2(P)/Tb * (0.25+0.25sum<n=inf>(e^(-j2nfpi*Tb)))