bidirectional transmission distribution
function (BTDF) the optical scattering func-
tion for transmissive optics. The scattering
function vs. angle is normalized to signal at
zero degrees and with respect to solid angle
of detector, including obliquity factor.
bifilar winding
a two-wire winding. It
is often utilized in stepper motors to permit a
unipolar power supply to produce alternating
magnetic poles by energizing only half of the
bifilar winding at any one time.
bifurcation
a term from Chaos Theory
referring to a sudden change in the qualitative
behavior of the solutions.
bifurcation diagram
a diagram where
the sampled variable is plotted versus a pa-
rameter. The sampling period is equal to the
source period. Similar to a Poincare map.
big endian
a storage scheme in which the
most significant unit of data or an address is
stored at the lowest memory address. For
example, in a 32-bit, or four-byte word in
memory, the most significant byte would be
assigned address
i, and the subsequent bytes
would be assigned the addresses:
i +1, i +2,
and
i + 3. Thus, the least significant byte
would have the highest address of
i + 3 in
a computer implementing the big endian ad-
dress assignment. “Big endian” computers
include IBM 360, MIPS R2000, Motorola
M68000, SPARC, and their successors.
The little endian approach stores the least
significant unit at the lowest address. (The
terms big endian and little endian are taken
from Jonathan Swift’s satirical story, Gul-
liver’s Travels.
See also
little endian
.
BIL
See
basic lightning impulse level
and
basic impulse insulation level
.
bilateral Laplace transform
a Laplace
transform of the form
L{f } =
Z
−∞
+∞f (t)e
−st
dt,
where
s is a complex number. See
Laplace
transform
.
bilateral Z-transform
a Z-transform of
the form
Zx =
+∞
X
n=−∞
x[n]z
−n
.
bilinear control systems
a class of non-
linear control system models that are linear
in state, output and control variables treated
separately but they contain the products of
those variables. Such models arose naturally
in modeling the number of chemical pro-
cesses where the controls are flow rates that
appear in the system equations as products
with state variables. The bilinear control sys-
tems may also be used to model population
dynamics perturbed by control actions which
enter growth equations as multipliers of state
variables. Bilinear control systems can arise
also in connection with adaptive control nom-
inally linear systems where uncertain pa-
rameters regarded as additional state vari-
ables leads to bilinear terms in model equa-
tions. Bilinear time-continuous control sys-
tems may be represented by the state equa-
tions having the form
˙x = Ax + Bu +
m
X
i=1
D
i
u
i
x
where
x is the state vector, u the control vec-
tor with components
u
i
, i = 1, 2, . . . , m,
A, B, D
i
are matrices of the appropriate di-
mensions. See also
population dynamics
.
bilinear interpolation
interpolation of a
value in 2-D space from four surrounding val-
ues by fitting a hyperbolic paraboloid. The
value at
(x, y), denoted f (x, y) is interpo-
lated using
f (x, y) = ax + by + cxy + d,
where
a, b, c and d are obtained by substitut-
ing the four surrounding locations and values
into the same formula and solving the system
of four simultaneous equations so formed.
c
2000 by CRC Press LLC