M-FSK
PHI(t) = Acos(2tpi*fi), i=<1,M>
fi = f1 + (i-1)delf

PSD looks sinish with pulse centers at each fi

want orthogonal signals, for example: int<0,T>(Acos(2tpi*fm)Acos(2tpi*fn))dt = 0 means that they're orthogonal
ends up being AA/2 * int<0,T>(cos(2tpi*(fn+fm)) + cos(2tpi*(fm-fn))) ~~ AA/2 * (sin(2Tpi*(fm-fn))/(2pi*(fm-fn))) = 0
need 2pi*(fm-fn)T, this means that if you space frequencies by 1/2T, the signals will be orthogonal

M-PSK
Si(t) = sqrt(2E/T)cos(wct + ((2i+1)/M)pi), i=0..M-1 = sqrt(2E/T)(cos(wct)cos((2i+1)pi/M) - sin(wct)sin((2i+1)pi/M))
cos piece of last eqn ^^ is the in phase component, the sin portion is the quadrature component

4-PSK is equivalent to 2 binary-ask sigs
organized in a circle around the origin, polar looking graph

Q-ASK aka QAM
M = M'M"
s(t) =Auicos(wct)+Avjsin(wct)
ui in {-(M'-1), -(M'-3)..-1,1,3..(M'-1)}
ditto for vi and M"

usually arranged in a rectangle, further from the origin means it takes more energy to send it

8QAM
ui in {-3,-1,1,3}
vi in {-1,1}

16QAM
ui in {-3,-1,1,3}
vi in {-3,-1,1,3}

oh shit...probability distribution functions
watch for mudkips
and lions

mu is mean, sigma^2 is the variance
PDF is prob density f(), probability that X lies between a and b
if mean is 0, variance is equal to avg normalized power

thermal noise
caused by thermal motion of electrons in all dissipative components
has following tendencies:
	mean is 0
	has gaussian PDF
	has avg normalized PSD that is constant=No/2 from DC to ~10^12Hz
	called additive white gaussian noise

filtering of random sigs
if a random sig with mean 0 goes through a LTI filter, the output will also have mean 0, but it will no longer be white noise. it will still be gaussian
gaussian function doesn't have a closed form integration
we use a tabulation instead
tabulation known as complementary error function aka Q function, values for mu=0, variance=1
Q(-a) = 1-Q(a)


performance criterion
transmitter input chosen from finite set of possible symbols
receiver obj: accurately det which symbol was transmitted
figure of merit: prob of error in decision, often interested in prob of bit error or bit error rate (BER)

general receiver
binary sig transmitted with thermal noise added to channel