Page 26 - Electrical Engineering Dictionary

mean any pair X ∈ R p×m [s], Y ∈ R q×m [s] The algorithm is based on the row compres-
satisfying the equation. The equation (1) sion of suitable matrices.
has a solution if and only if the matrices
[A, B, C] and [A, B, 0] are column equiva- 2-D Z-transform F(z 1 ,z 2 ) of a dis-
lent or the greatest common left divisor of A crete 2-D function f ij satisfying the condi-
and B is a left divisor of C. The 2-D equation tion f ij = 0 for i< 0 or/and j< 0is
defined by
AX + YB = C (2)
∞ ∞
X X −i −j
A ∈ R k×p [s], B ∈ R q×m [s], C ∈ R k×m [s] F (z 1 ,z 2 ) = f ij z z 2
1
are given, is called the bilateral 2-D polyno- i=0 j=0
mial matrix equation. By a solution to (2) we An 2-D discrete f ij has the 2-D Z-transform
mean any pair X ∈ R p×m [s], Y ∈ R k×q [s] if the sum
satisfying the equation. The equation has a
∞ ∞
solution if and only if the matrices X X −i −j
f ij z z
1 2
i=0 j=0
A 0 AC
and
0 B 0 B exists.
are equivalent.
2DEGFET See high electron mobility
transistor(HEMT).
2-D Roesser model a 2-D model de-
scribed by the equations
2LG See double phase ground fault.
" h # " h #
x x
i+1,j = A 1 A 2 ij + B 1 3-dB bandwidth for a causal low-pass
x v A 3 A 4 x v B 2 u ij
i,j+1 ij or bandpass filter with a frequency function
i, j ∈ Z + (the set of nonnegative integers), H(jω) the frequency at which | H(jω) | dB
is less than 3 dB down from the peak value
" #
x h | H(ω P ) |.
y ij = C ij + Du ij
v
x
ij 3-level laser a laser in which the most
Here x h ∈ R n 1 and x v ∈ R n 2 are the hori- important transitions involve only three en-
ij ij
zontal and vertical local state vectors, respec- ergy states; usually refers to a laser in which
m
tively, u ij ∈ R is the input vector, y ij ∈ R p the lower level of the laser transition is sepa-
is the output vector and A 1 , A 2 , A 3 , A 4 , B 1 , rated from the ground state by much less than
B 2 , C, D are real matrices. The model was the thermal energy kT. Contrast with 4-level
introduced by R.P. Roesser in “A discrete laser.
state-space model for linear image process-
ing,” IEEE Trans. Autom. Contr., AC-20, 3-level system a quantum mechanical
No. 1, 1975, pp. 1-10. system whose interaction with one or more
electromagnetic fields can be described by
2-D shuffle algorithm an extension of the considering primarily three energy levels.
Luenberger shuffle algorithm for 1-D case. For example, the cascade, vee, and lambda
The 2-D shuffle algorithm can be used for systems are 3-level systems.
checking the regularity condition
4-level laser a laser in which the most
det [Ez 1 z 2 − A 0 − A 1 z 1 − A 2 z 2 ] 6= 0 important transitions involve only four en-
ergy states; usually refers to a laser in which
forsome(z 1 ,z 2 ) ∈ C×C ofthesingulargen- the lower level of the laser transition is sep-
eral model ( See singular 2-D general model). arated from the ground state by much more

c
2000 by CRC Press LLC