Digital Signal Processing Reference
In-Depth Information
performance, but the computational complexity of the latter is much lower than
that of the former.
The remainder of this chapter is organized as follows: In Section 6.2, we
review the 2-D nonparametric APES algorithm. In Section 6.3, we present 2-D
extensions of the MAPES-EM algorithms and develop the 2-D MAPES-CM al-
gorithm in Section 6.4. In Section 6.5, we compare MAPES-CM with MAPES-
EM,from both theoretical and computational points of view. Numerical examples
are provided in Section 6.6 to demonstrate the performance of the MAPES algo-
rithms.
6.2 TWO-DIMENSIONAL ML-BASED APES
In this section we provide the 2-D extension of APES, devised via a ML fitting
based approach, for complete-data spectral estimation.
Consider the 2-D problem introduced in Section 3.3.1. Partition the
N
1
×
N
2
data matrix
y
0
,
0
y
0
,
1
···
y
0
,
N
2
−
1
y
1
,
0
y
1
,
1
···
y
1
,
N
2
−
1
Y
(6.1)
.
.
.
.
.
.
y
N
1
−
1
,
1
···
y
N
1
−
1
,
N
2
−
1
y
N
1
−
1
,
0
into
L
1
L
2
overlapping submatrices of size
M
1
×
M
2
:
y
l
1
,
l
2
y
l
1
,
l
2
+
1
···
y
l
1
,
l
2
+
M
2
−
1
y
l
1
+
1
,
l
2
y
l
1
+
1
,
l
2
+
1
···
y
l
1
+
1
,
l
2
+
M
2
−
1
Y
l
1
,
l
2
=
,
(6.2)
.
.
.
.
.
.
y
l
1
+
M
1
−
1
,
l
2
y
l
1
+
M
1
−
1
,
l
2
+
1
···
y
l
1
+
M
1
−
1
,
l
2
+
M
2
−
1
where
l
1
=
0
, ... ,
L
1
−
1
,
l
2
=
0
, ... ,
L
2
−
1
,
L
1
N
1
−
M
1
+
1,
and
L
2
1. Increasing
M
1
and
M
2
typically increases the spectral resolution
at the cost of reducing the statistical stability of the spectral estimates due to the
N
2
−
M
2
+
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