Digital Signal Processing Reference
In-Depth Information
(a)
(b)
(c)
(d)
(e)
(f)
(g)
(h)
FIGURE 5.12
Myriadizing a linear bandpass filter in an impulsive environment: (a) chirp signal, (b) chirp in
additive impulsive noise, (c) ideal (no-noise) myriad smoother output with
K
=∞
, (e)
K
=
0
.
5,
and (g)
K
=
0
.
2; myriad filter output in the presence of noise with (d)
K
=∞
, (f)
K
=
0
.
5, and
(h)
K
=
0
.
2.
by further reducing
K
to 0
2, or lower, as the filter in this case is driven to a
“selection” operation mode.
.
5.10.2
Optimization
The
optimization
of the weighted myriad filter parameters for the case when
the linearity parameter
K
satisfies
K
0 was first described in Reference 30.
The goal is to design the set of weighted myriad filter weights that optimally
estimate a desired signal according to a
statistical error criterion
. Although the
mean absolute error (MAE) criterion is used here, the solutions are applicable
to the mean square error (MSE) criterion with simple modifications.
Given an input (observation) vector
X
>
,X
N
]
T
,aweight vector
=
[
X
1
,X
2
,
...
=
,W
N
]
T
, and linearity parameter
K
, denote the weighted
myriad filter output as
Y
W
[
W
1
,W
2
,
...
≡
Y
K
(
W
,
X
)
, sometimes abbreviated as
Y
(
W
,
X
)
.
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