Electrical Engineering Dictionary - part 80

The simplest way to introduce perturbations
to the dynamics represented by affine con-
trol actions is to add a bilinear term into the
Gompertz equation

˙x = gln

max

− kux

where

u is a control variable and k represents

a perturbed population loss (or growth) pa-
rameter. By applying the dimensionless scal-
ing, the equation could be once more trans-
formed into the linear one with respect to
variable

y. The unperturbed Gompertz dy-

namics could also be represented by two first-
order differential linear equations

˙x = q(t)x; ˙q = −gq; x(0) = x

; q(0) = q

with

−

= x

max

Gordon–Haus limit

expresses the max-

imum performance of a soliton-based com-
munication system as a bitrate-length prod-
uct.

GOS

See

grade of service

governor

a device connected to a rotat-

ing machine by which the speed-regulating
system is automatically adjusted to maintain
constant speed under various load conditions.

governor power flow

the inherent re-

sponse of prime movers or governors to a
change in the operating condition of the
power system in an attempt to balance the
power equation. All generators participate at
some level in the change, with larger gener-
ators picking up relatively larger amounts.

GPS

See

global positioning system

grade of service (GOS)

a probabilistic

measure of service or equipment availability
in a telecommunications network, expressed
as the probability of a particular service (e.g.,
a completed telephone connection) being de-
nied at request time.

graded index

medium in which the index

of refraction varies as a function of position;

usually refers to variations transverse to the
direction of propagation, and quadratic trans-
verse variations are especially important.

graded index fiber

an optical fiber where

the core refractive index varies from a maxi-
mum at its center to a minimum value at the
core-cladding interface. The profile is typ-
ically designed so that all modes of a mul-
timode fiber propagate at approximately the
same velocity. See also

step index fiber

graded index lens

cylindrical optical el-

ements with a refractive-index profile across
the cross section of the element to provide the
transfer; lens in which the transmitted waves
are focused or defocused by transverse vari-
ations of the index of refraction rather than
by transverse variations of the thickness.

graded index optical fiber

an optical

fiber with a refractive index in the core
that decreases monotonically from the fiber
axis to the interface between the core and
cladding.

The index usually goes from

a higher value in the center of the core
to a lower value of refractive index at the
core/cladding interface.

See also

graded

index profile

graded index optics

optical elements that

use a refractive-index profile across the cross-
section of the element, typically a cylinder,
to provide particular transfer functions as for
lenses; the profile is generally produced by
ion implantation. Also called GRIN optics.

graded index profile

an index of refrac-

tion in an optical fiber core that decreases
with distance from the core axis out to the
core/cladding boundary. The variation of the
index of refraction with the radial distance
from the fiber axis can be given approxi-
mately as a power law.

gradient

a vector function denoted by

∇f

or grad

f , where f is a continuous, differ-

entiable scalar function. For a 2-D function

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f (x, y), the gradient is

∇f =




∂f

∂x
∂f

∂y




The magnitude of this gradient is

|∇f | =

∂f
∂x

∂f
∂y

In image processing, the term gradient often
refers to the magnitude of the gradient. See
also

Sobel operator

gradient descent

a method for finding

the minimum of a multidimensional function
f (x). The technique starts at some point and
advances towards the minimum by iteratively
moving in a direction opposite to that of the
gradient:

i+1

= x

− α

∂f
∂x

where

α is some scalar, usually set empiri-

cally. See also

gradient

optimization

gradient edge detector

an edge detec-

tor that defines an edge to be present at a
pixel only if the magnitude of the gradient at
that pixel is greater than some threshold. See
also

gradient index optics

optical compo-

nents, e.g., optical fibers, within which the
refractive index changes gradually between
two extremes.

gradient space

a 2-D representation of the

orientation of a 3-D surface in space, in which
the two components of a point

P ≡ (p, q) are

the first-order partial derivatives of a surface
of the form

z = f (x, y).

Gram-Schmidt orthogonalization

a re-

cursive procedure for whitening (decorrelat-
ing) a sequence of random vectors. See also

whitening filter

grammar

an ordered 4-tuple

(G =

T , V, P, S), where T is said to be the set of
terminals,

V is the set of variables or non-

terminals,

P a set of production rules and

S ∈ V is called the start symbol. Terminals
are the symbols with which the strings of the
language are made. For example,

T may be

the English alphabet, the ASCII character set,
or the set

{0, 1}. Non-terminals are symbols

that are replaced by a string of zero or more
terminals and non-terminals. The production
rules specify which strings can be used to re-
place non-terminals. The symbol

S is the first

symbol with which every production starts.
All the strings that can be generated from

using rules in

P are said to be in L(G), the

language of

example: Let

G be the grammar (T , V, P, S)

such that

T = {a, b}

V = {S}

where

S is the start symbol and

P = {S → aSb, S → }

where

is the empty string. The language

L(G) is the set of all strings of the form

. The

→ symbol signifies that S can

be replaced with whatever follows the arrow.

grant signal

a control signal on a bus that

gives permission to control the bus to another
module.

graph

a couple

G = (E, V ) where V is

a set of nodes and

E ⊆ V × V is a set of

edges. Graphs are widely used in modeling
networks, circuits, and software.

graph search

an optimization technique

used to find the minimum cost path from a
starting point to a goal point, through a graph
of interconnected nodes. Each link between
nodes has an associated path cost, which must
be selected based on the problem of interest.
See also

optimization

2000 by CRC Press LLC

graphic adapter

an adapter for inter-

facing the computer toward a monitor. See

graphic controller

See

graphic adapter

graphical kernel system (GKS)

a stan-

dard for computer graphics recognized by
both ANSI and ISO. GKS defines the ma-
nipulation of graphic objects, including their
visualization, print, etc. All manipulation is
performed by regarding the graphic adoption
as a independent device driver. In this way,
GKS applications can be executed on differ-
ent kinds of graphics adapters.

graphics

the discipline dealing with the

generation of artificial images by a computer.
Its two main aspects are geometric modeling,
whose subject is the computational represen-
tation of the geometry and topology of ob-
jects and scenes, and rendering, which stud-
ies the generation of images from the interac-
tion of light and objects. Graphics has been
generalized to the synthesis of animated im-
age sequences, in which case one speaks of
computer animation. Also called computer
graphics, image synthesis.

Graphics Interchange Format (GIF)

popular image-file format that compresses
the image with LZW coding.

See also

The Graphics Interchange Format(c) is the

grating

See

diffraction grating

grating lobe

a lobe in an antenna radiation

pattern whose peak amplitude is equal to that
of the main lobe.

grating spectrometer

an instrument that

provides a spectral decomposition of a opti-
cal source using a diffraction grating to give
spatial dispersion of wavelengths.

gravitational torque

torque that depends

upon the position of the robot in the gravita-
tional field.

Gray book

See

IEEE Color Books

Gray code

a code in which each of a

sequence of code words differs by one bit
from the preceding one, and the assigned
value of each code word is one more than
that of the preceding one.

Such a code

avoids glitches (i.e., sharp momentary un-
wanted spikes) when, in an electromechani-
cal system, the sensors giving the code words
are imperfectly aligned. For example, one
possible three-bit Gray code is:

000 001 011 010 110 111 101 100

gray level

the individual numerical value

corresponding to a particular degree of
brightness in a digital image, often on an 8-
bit gray scale consisting of 256 gray levels
stretching from pure black to pure white.

gray level co-occurrence

a means of

measuring texture and other brightness varia-
tions in digital images by generating matrices
which tabulate the frequencies with which
different gray levels co-exist at different dis-
tance vectors from each other.

gray level saturation

the restriction of

image gray scale so that intensities above a
certain level become fixed at the white level
corresponding to the highest numerical value
available within the current storage capacity,
typically one byte, of each pixel.

gray scale

(1) an optical pattern in discrete

steps between light and dark.

(2) intrinsic modulation property of the

marking technology that enables dots of ei-
ther different size or intensity to be printed.

(3) in digital images, a method used to

represent varying levels of brightness. Typi-
cally, gray images use 8-bit gray level for the
gray scale so that for each picture element, 0
represents pure black and 255 represent pure

2000 by CRC Press LLC

Gray code

decimal digit

Gray code

000

001

011

010

110

111

white with other gray levels in between these
extremes.

grayscale

See

gray scale

Green book

See

IEEE Color Books

Green’s function

the function that satis-

fies a given differential equation having as
source term a Dirac delta function. See

delta

function

Green’s theorems

consider a closed, reg-

ular, surface

S bounding a volume V where

the two scalar functions

φ and ψ, continuous

together with their first and second deriva-
tives throughout

V and on the surface S, are

defined. Green’s first identity states

∇ψ · ∇φ dV +

ψ∇

φ dV =

∂φ

∂n

while Green’s second identity takes the form

ψ∇

φ − φ∇

∂φ

∂n

dS −

∂ψ

∂n

which is frequently referred to as Green’s the-
orem.

grey level

See

gray level

grey scale

See

gray scale

grid

refers to the regular array of vertical

and horizontal wires used for interconnecting
the chip.

grid array

a technique for combining the

output of amplifiers or oscillators in space
by using a two-dimensional spatial array of
elements placed on a uniformly spaced grid.

GRIN optics

See

graded index optics

grip

a twisted wire tie which secures a

wire to an insulator or other fixture.

grip teeth

a set of jaws which secures a

wire to a hoist or come-a-long cf so that it can
be pulled into place.

gripple

See

gain ripple

grooved media

on an optical disk, the

embossment of the disk surface with grooves
such that the disk tracks are either the grooves
themselves or the regions between the groves.

ground

(1) an earth-connected electrical

conducting connection that may be designed
or non-intentionally created.

(2) the electrical “zero” state, used as the

reference voltage in computer systems.

ground bounce

a transient variation in the

potential of the ground terminal of a logic de-
vice caused by variations in the supply cur-
rent acting on the ground impedance of the
circuit as seen by the device. Usually caused
by simultaneous turnon of the pullup and
pulldown sections of totem-pole outputs.

ground bounce noise

ground bounce oc-

curs when a large number of semiconduc-
tor circuit components are mounted on a
common semiconductor chip substrate, so
that they are imperfectly insulated from each
other.

In normal operation the substrate

should act as an insulator; however, during
certain unusual fluctuations in signal levels,
the systems power and ground connections
can experience fluctuations, which affect the
performance of each component in a ran-
dom way that has the characteristics of noise,
much like capacitive coupling.

2000 by CRC Press LLC

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