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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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df parameter in FM system (frequency deviation)
i0(t) optimum MMSE estimate
ds(t, a(t)) derivative of s(t, a(t)) with respect to a{t)
d(t) error in desired point estimate
d+(t) output of arbitrary nonlinear operation
8 phase of specular component (Rician channel)
interval in PFM detector
d change in performance index
Adx desired change in d
AiV change in white noise level
constraint on covariance function error
Am mean difference vector (i.e., vector denoting the dif-
ference between two mean vectors)
AQ matrix denoting difference between two inverse co-
variance matrices
E energy (no subscript when there is only one energy in
the problem)
Ea expectation over the random variable a only
Ee(N) energy in error waveform (as a function of the number
of terms in approximating series)
?/ energy in interfering signal
E{ energy on ith hypothesis
Er expected value of received energy
Et transmitted energy
Ey energy in y(t)
Glossary 675
El9 Eq energy of signals on and H0 respectively
E energy in error signal (sensitivity context)
eN(t) error waveform
j interval error
T total error
erf () error function (conventional)
erf* () error function (as defined in text)
erfc () complement of error function (conventional)
erfc* () complement of error function (as defined in text)
) (eta) threshold in likelihood ratio test
?() expectation operation (also denoted by () infrequently)
F function to minimize or maximize that includes
Lagrange multiplier f(t) envelope of transmitted signal
f(t) function used in various contexts
fit: r(u),
ҳ < < Tf) nonlinear operation on r(u) (includes linear operation
as special case) fc oscillator frequency (toc
/(0 normalized difference signal
F matrix in differential equation
F(t) time-varying matrix in differential equation
Fd(t) matrix in equation describing desired signal
&+) factor of Sr(oj) that has all of the poles and zeros in
LHP (and \ of the zeros on jw-axis). Its transform is zero for negative time. g(t) function in colored noise correlator
g(t, A), g(t, A) function in problem of estimating A (or A) in colored
g(Xi) a function of an eigenvalue
gh(t) homogeneous solution
g{(r) filter in loop
gio(r), Gl0(jw) impulse response and transfer function optimum loop
gpjj) unrealizable post-loop filter
gpuo(T), Gpuo{jw) optimum unrealizable post-loop filter
g6(t) impulse solution
#(0 difference function in colored noise correlator
g\ a weighted sum of g(Af)
goo(0> Gao(J<*>) infinite interval solution
676 Glossary
G matrix in differential equation
G(0 time-varying matrix in differential equation
Gd linear transformation describing desired vector d
Gd(0 matrix in differential equation for desired signal
g(0 function for vector correlator
ga(A) nonlinear transformation describing desired vector d
() Gamma function
parameter (y = kV\ + A)
threshold for arbitrary test (frequently various constants
absorbed in y)
a factor in nonlinear modulation problem which controls
the error variance
H0, Hl9..., { hypotheses in decision problem h(t9 u) impulse response of time-varying filter (output at t due
to impulse input at u)
^ch(*> tt) channel impulse response
hL(t) low pass function (envelope of bandpass filter)
h0(t9 u) optimum linear filter
W0(r)9 H'0(jo>) optimum processor on whitened signal: impulse
response and transfer function, respectively h0Jj)9 H0U(jco) optimum unrealizable filter (impulse response and
transfer function) hw(t9 u) whitening filter
(, ) arbitrary linear filter
h*(t9 u) linear filter in uniqueness discussion
H linear matrix transformation
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