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Detection, Estimation modulation theory part 1 - Vantress H.

Vantress H. Detection, Estimation modulation theory part 1 - Wiley & sons , 2001. - 710 p.
ISBN 0-471-09517-6
Download (direct link): sonsdetectionestimati2001.pdf
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P operator to denote d/dt (used infrequently)
Po fixed probability of interval error in PFM problems
˳*,( probability density of r, given that Hi is true
Px,(Xt) or probability density of a random process at time t
Pxt{X'. t)
m /th coordinate function, ith eigenfunction
() moment generating function of random variable x
m phase of signal
MO low pass phase function
P(0 cross-correlation matrix between input to message
?f, r) generator and additive channel noise
state transition matrix, time-varying system
state transition matrix, time-invariant system

Pr[.], Pr(.) probability of event in brackets or parentheses
(, Marcums Q function
Gn(', w) inverse kernel
height of scalar white noise drive
Q covariance matrix of vector white noise drive (Section
Q 6.3)
inverse of covariance matrix
Qi, Qo inverse of covariance matrix Kl5 K0
Qn(w, Z) inverse matrix kernel
R rate (digits/second)
Rx(t, m) correlation function
&(</(*), 0 risk in point estimation
^-abs risk using absolute value cost function
Bayes risk
680 Glossary
risk using fixed test
risk using mean-square cost function
^unf risk using uniform cost function
received waveform (denotes both the random process
and a sample function of the process)
rc(.t) combined received signal
ra(0 output when inverse kernel filter operates on r(t)
(1) term approximation
r*( 0 output of whitening filter
*(0 actual output of whitening filter (sensitivity context)
r**(0 output of SQ((x)) filter (equivalent to cascading two
whitening filters)
Pli normalized correlation s^t) and Sj(t) (normalized signals)
Pl2 normalized covariance between two random variables
R(0 covariance matrix of vector white noise w(0
R correlation matrix of errors
*, error correlation matrix, interval estimate
r, R observation vector
', ] radial prolate spheroidal function
S(jo>) Fourier transform of s(t)
Sc(co) spectrum of colored noise
Sonl, ] angular prolate spheroidal function
^(oj) Fourier transform of Q(t)
Sr(cu) power density spectrum of received signal
power density spectrum
S'eoO) transform of optimum error signal
signal component in r(t), no subscript when only one
s(t, ) signal depending on A
j(*, (0) modulated signal
Sa(!) actual s(t) (sensitivity context)
Sl{t) interfering signal
SiaiO actual interfering signal (sensitivity context)
Si coefficient in expansion of s(t)
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