learning more about amplitude shift keying, when shifting to +/- fc, there is no impulse at fc, so the carrier is supressed
method of recovering the message sig is called synchronous detection or coherent detection where a carrier of the exact freq and phase is sued in the demodulation process

AM world:
in order to avoid having to gen a replica of the carrier based on the received sig, AM transmits a carrier along with the modulated signal: AM(t) = (A+m(t))cos(wc*t)
the constant A generates impulses at f+fc and f-fc with amp A/2

envelope of an AM sig is mag(A+m(t))
if A is chosen such that A+m(t) > 0 for all t, the envelope shape can be used for envelope detection
the modulation index mu is  mp/A
power is A/2

ex:
as long as A+m(t) > 0, there is no zero-crossing of the envelope
if there is a zero-crossing of the envelope, it generates a phase reversal of the carrier for each zero crossing, also, the envelope detector will only grab the abs of the sig

BW efficient AMs
the DSB spectrum wastes BW
more efficient use of the spectrum with QAM or SSB (LSB or USB) to cut the BW in half


QAM ops by xmitting 2 dsb sigs via carriers of teh same freq, but in phase quadrature
QAM = m1(t)cos(wc*t) + m2(t)sin(wc*t)
received sig is demodulated by multiplying by sin and cos separately to pull out the two sigs, then through a low pass filter to get the message back out

ex4-4:
thetaqam(t) = m1cos(wct) + m2sin(wct)
x1(t) = thetaqam(t)2cos(wct) = m1(t) + m2(t)

nonlinear modulation:
consider a generalized sinusoidal sig phi(t) = Acos(theta(t))
theta(t) = wct+theta0
over a small interval delt, the angular freq of phi(t)

theta'(t) = wi gives you instantaneous freq
theta(t) = int<-inf,t>(wi(alpha)dalpha)
in phase mod (PM), the angle theta(t) is varied linearly with m(t), theta(t) = wct + kp*m(t)

PM = Acos(wct+kp*m(t))
in PM, the inst ang freq varies linearly with the derivative of the modulation sig

in FM, the inst freq varies linearly with the modulating signal
wi(t) = wc+kf*m(t)
theta(t) = wct+kf*int<-inf,t>(m(alpha)dalpha)