Page 285 - Electrical Engineering Dictionary

wherein the differential equation is replaced moving average process can be written as the
by a finite difference equation that relates the output of a FIR filter driven by white noise.
value of the solution at a point to the values See also impulse function, moving
at neighboring points. average, infiniteimpulseresponse(IIR)filter.
See recursive filter.
finite difference time domain (FDTD) a
numerical technique for the solution of elec- finite state machine (FSM) a mathemat-
tromagnetic wave problems that involves the ical model that is defined in discrete time and
mapping of the Maxwell equations onto a fi- has a finite number of possible states it can
nite difference mesh and then following the reside in. At each time instance, an input,
time evolution of an initial value problem. x, is accepted and an output, y, and a transi-
This technique is widely used to investigate tion from the current state, S c , to a new state,
the performance of a complex RF structures. S n , are generated based on separate functions
of the input and the current state. A finite
finite differences a method used to nu- state machine can be uniquely defined by a
merically solve partial differential equations set of possible states, S, an output function,
by replacing the derivatives with finite incre- y = f(x, S c ), and a transition function, S n =
ments. g(x, S c ). An FSM describes many different
concepts in communications such as convo-
finite element a numerical technique for lutional coding/decoding, CPM modulation,
the solution of boundary value problems that ISI channels, CDMA transmission, shift-
involves the replacement of the set of differ- register sequence generation, data transmis-
ential equations describing the problem un- sion and computer protocols. Also known as
der consideration with a corresponding set finite state automata (FSA), state machine.
of integral equations. The area or volume of
the problem is then subdivided with simple finite state VQ (FSVQ) a vector quan-
shapes such as triangles and an approxima- tizer with memory. FSVQ form a subset of
tion to the desired solution with free parame- the general class of recursive vector quanti-
ters is written for each subregion and the re- zation. The next state is determined by the
sulting set of equations is minimized to find current state S n together with the previous
the final solution. This approach is useful channel symbol u n by some mapping func-
for solving a variety of problems on complex tion.
geometries.
S n+1 = f (u n ,S n ) ,n = 0, 1,...
finite field a finite set of elements and two
operations, usually addition and multiplica- Thisalsoobeystheminimumdistortionprop-
tion, that satisfy a number of specific alge- erty
braic properties. In honor of the pioneering
work by Evariste Galois, finite fields are of- −1
ten called Galois fields and denoted GF(q), α(x,s) = min d(x, β(u, s))
whereq isthenumberofelementsinthefield.
Finite fields exist for all q which are prime with a finite state S =[α 1 ,α 2 ,...,α k , such
or the power of a prime. that the state S n can only take on values in S.
The states can be called by names in gener-
finite impulse response (FIR) filter any ality.
filter having an impulse response that is
nonzero for only a finite period of time (there- finite wordlength effect any perturbation
fore having a frequency response consisting of a digital filter output due to the use of fi-
only of zeros, no poles). For example, every nite precision arithmetic in implementing the

c
2000 by CRC Press LLC