Page 324 - Electrical Engineering Dictionary

germanium (Ge) an optical material for Gibbs phenomenon the rippling phe-
construction of components and systems at nomenon in the reconstruction of a function
infraredwavelengths, especiallyinthe8to14 around a discontinuity based on the Fourier
micron region. Also, an acousto-optic mate- series of the function. Specifically, given a
rial for infrared wavelengths. discontinuous periodic function f which is
square-integrable on its period, the Fourier
Gershgorin circle measures the relative series of f converges to f in the square mean
size of the off-diagonal elements in a transfer sense. When the periodic function corre-
function matrix at a given frequency. When sponding to the n first terms of that Fourier
evaluated over a range of frequencies, these series is built, then ripples appear at the vicin-
circles sweep out a band, centered on the ity of each discontinuity of f . When n tends
diagonal elements, that is used in the pre- to infinity, these ripples tend to zero in the
diction of closed loop stability for multi- square mean sense, but their maximum am-
input–multi-output systems. This theory is plitude does not tend to zero; this produces
based on Gerhsgorin’s theory on the bounds an overshoot by a factor of 1.1789797 and
of matrix eigenvalues. See also diagonal an undershoot by a factor of 0.9028233. A
dominance and inverse Nyquist array. similar effect arises for a square-integrable
nonperiodic function reconstructed from its
Fourier transform. The phenomenon causes
GFCI See ground-fault circuit interrupter.
ringing around edges in low bit rate image
coding. See Fourier integral, Fourier series,
norm.
GFI See ground fault interrupter.
Gibbs random field a class of random
GFLOP See gigaflop.
fields described by normalized exponentials
of potential functions over cliques. Let S =
ghosting the formation of an image in s 1 ,s 2 ,... be points on a lattice, and let ω ∈ 
which a ghost image (i.e., a similar, fainter, be a sample of a random field on this lattice.
slightly displaced image) appears superim- Points on the lattice interact with other lattice
posed on the intended image; ghosts result points in a local, predefined manner; that is,
from a form of crosstalk, and typically arise the energy of the lattice is given by the sum
by radio transmission via an alternative path of the energies of locally-interacting sets of
occurring as a result of random reflection. points in the lattice: each such set of points
is known as a clique C ∈ C. Specifically,
giant magnetoresistance effect huge the energy of clique C in sample ω is V C (ω),
change in electrical resistance with relatively where V is a potential function depending
small change in magnetic field exhibited by only upon the points in C. Then the total
multilayers of many combinations of metal- energy of a sample ω is given by
lic materials. Used in the next generation of
X
hard disk memory. E(ω) = V C (ω).
C∈C
giant pulse large output pulse from a
With this definition, a probability measure π
laser oscillator that results when the cavity
is a Gibbs random field if
losses are quickly raised from a high value
holding a pumped laser below threshold to 1 −E(ω)/T
low value bringing the laser above threshold π(omega) = e
Z
(Q-switching or loss-switching) or when the
P −E(ω)/T
gain occurs in the form of a short pulse (gain where Z = ω e is a normalization
switching). constant.

c
2000 by CRC Press LLC