250 ◾ Abhijit Patil, Rajesh Langoju, and Pramod Rastogi
From Equation (7.23), we observe that the transformation in Equation
(7.23) is rotation. is property plays a signicant role in spectral estima-
tion. Hence, using the same analogy as in Equation (7.23), we can derive
the matrices S
1
and S
2
from the S matrix as
=
−×
×
−× −× −
−×
−×
mm m
mmm
mf
mf
S0
.
1(1) (1)(1) 1
2(1) 1(1) (1)
(1)
(1)
(7.24)
We can thus represent the matrix S
2
using Equations (7.21) and (7.24) as
−
1
(7.25)
where
. It is important to note that because both matrices S and
A in Equation (7.21) have full column rank, the matrix Γ is nonsingular.
e matrices A
1
and A
2
in Equation (7.23) have full column rank (equal
to f) because matr