Page 130 - Electrical Engineering Dictionary

characterrecognition Seeopticalcharacter useful in the analytic computation of higher
recognition. order moments and convolutions of probabil-
ity densities.
character string (1) a series of continu-
ous bytes in memory, where each byte repre- characteristic impedance inherent prop-
sents one character. erty of a transmission line that defines the
(2) data structure corresponding to or- impedance that would be seen by a signal
dered sequence of characters. if the transmission line were infinitely long.
If a signal source with a “source” or “refer-
characteristic equation the polynomial ence” impedance equal to the characteristic
equation that results when the characteristic impedance is connected to the line there will
function is equated to zero. Its roots gives the be zero reflections.
singularities of the transfer function model,
which in turn determine its transient behav- characteristic loci the plots of the eigen-
ior. Specifically, any root of the character- values of transfer function matrices, eval-
istic equation that has a negative real part uated over a range of frequencies. These
indicates a stable decaying transient, while traces, which are parametrized by frequency,
any root with a positive real part indicates an are shown on a single Nyquist plot and
unstable growing transient. Any root with used to predict the closed loop stability of
zero real part indicates a marginally stable multiinput-multioutput systems, by applica-
transient that neither decays nor grows. The tion of the principle of the argument for com-
imaginary part of the root gives the frequency plex variable functions. Unlike the Nyquist
of oscillation of the transient signal. See also plots for single-input-single-output systems,
characteristic function. an individual eigenvalue might not encircle
the plane an integral number of times, yet the
characteristic function (1) the name total encirclements of all the eigenvalues will
given to the denominator polynomial of a be an integral number.
transfer function model. Through partial
fraction expansion of a transfer function and characteristic polynomial and equation of
subsequent inverse Laplace transformation, generalized 2-D model the determinant
it is obvious that the characteristics of the
system dynamics are defined by this func- p (z 1 ,z 2 )
tion. For example, the transfer function
= det [Ez 1 z 2 − A 0 − A 1 z 1 − A 2 z 2 ]
9 n 1 n 2
g(s) = X X i j
6 + 5s + s 2 = a ij z z
1 2
has characteristic function i=0 j=0
2
φ(s) = 6 + 5s + s = (s + 2)(s + 3) (n 1 ,n 2 ≤ rank E) is called the 2-D char-
acteristic polynomial of the generalized 2-D
so its output response will contain terms like
model
−2t −3t
y(t) = αe + βe + ...
that are characteristic of the system itself. Ex i+1,j+1 = A 0 x ij + A 1 x i+1,j + A 2 x i,j+1
(Other terms in the response are attributed + B 0 u ij + B 1 u i+1,j + B 2 u i,j+1
to the forcing input signal.) See also
characteristic equation. i, j ∈ Z + (the set of nonnegative integers)
n
(2) a transformed probability density where x ij ∈ R is the semistate vector, u ij ∈
m
function, R is the input vector, and E, A k ,B k (k =
0, 1, 2) are real matrices with E possibly sin-
h i
T
8 x (ω) = E exp(jω x) gular or rectangular.
c
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