US 2010/0299381 A1Published application

Algorithm for the Adaptive Infinite Impulse Response Filter

AssigneeAulac Technologies Inc.

InventorKy Minh Vu

Life of this patent

Estimating the term…

Abstract

A new method to adjust the parameters of an adaptive Infinite Impulse Response (IIR) filter is suggested. The method adjusts the set of parameters of the pole polynomial of the filter. The parameters of the zero polynomial are calculated from the parameters of the pole polynomial. For efficiency, the pole polynomial is factored into a product of polynomials with at most quadratic order. To guarantee that the global minimum is achieved all the time, the algorithm ascertains that the new set of pole parameters gives smaller variance of the error than the set of pole parameters of the last adaptation time and the algorithm starts with the set of parameters that gives the global minimum.

Claims5

Dependent claims

A method to design and set up variables for the adaptive IIR filter with the following transfer function:

y
t
=
a

(
z
-
1
)
c

(
z
-
1
)

x
t
-
f
+
e
t
,
=
∑
i
=
0
m


a
i

z
-
i
1
+
∑
i
=
1
n


c
i

z
-
i

x
t
-
f
+
e
t
for minimal variance of the output error et weighted with a forgetting factor 0<λ≦1, which consists of the following steps:
(a) factoring the filter's pole polynomial as
c

(
z
-
1
)
=
(
1
+
b
0

z
-
1
)

∏
j
=
1
l


(
1
+
b
1
,
j

z
-
1
+
b
2
,
j

z
-
2
)
,
(b) setting up appropriate matrices and vectors of the variables, in the beginning and at each adaptation time t, for the said filter as below
C
1
=
[
c
l
⋯
c
1
⋱
⋮
c
l
⋮
0
⋮
]
C
2
=
[
1
⋮
1
c
l
⋯
1
⋱
⋱
⋱
⋱
⋱
⋱
c
l
⋯
1
]

c
=
[
c
1
⋮
c
l
]

X
t
=
[
x
t
0
x
t
0
+
1
⋮
⋮
⋮
x
t
]

y
t
=
[
y
t
0
-
l
⋮
y
t
0
⋮
⋮
y
t
]
with
Xt=[χt-fχt-f-1 . . . χt-f-m],
(c) setting up the variance of the output error et at the time t as
V
t

(
c
)
=
1
t

lim
.
ɛ
→
0

y
t
T

[
C
1
T
C
2
T
]

[
C
1

C
1
T
+
C
2

C
2
T
+
X
t

X
t
T
ɛ
]
-
1

[
C
1
C
2
]

y
t
if


λ
=
1


or
V
t

(
c
)
=
1
t

lim
.
ɛ
→
0
y
t
T

[
C
1
T
C
2
T
]

[
C
1

Λ
1
-
1

C
1
T
+
C
2

Λ
2

C
2
T
+
X
t

X
t
T
ɛ
]
-
1

[
C
1
C
2
]

y
t
and
Λ
1
=
[
λ
k
+
l
-
1
⋱
λ
k
]
,
Λ
2
=
[
λ
k
-
1
⋱
⋱
λ
2
λ
1
]
-
1
with k as the dimension of C2 otherwise.

379 more elements

A method to obtain the two real-valued parameters of a positive polynomial function ƒ(c1, c2) of these parameters that give the minimal value for the function, which consists of the following steps:

(a) setting the derivatives of ƒ(c1, c2) with respect to the parameters to zeros to produce two polynomial equations in two parameters:
g
1

(
c
1
,
c
2
)
=
∂
f

(
c
1
,
c
2
)
∂
c
1
=
∑
k
=
0

∑
l
=
0

a
k
,
l

c
1
k

c
2
l
=
0
g
2

(
c
1
,
c
2
)
=
∂
f

(
c
1
,
c
2
)
∂
c
2
=
∑
k
=
0

∑
l
=
0

b
k
,
l

c
1
k

c
2
l
=
0
,
(b) eliminating the parameter c2 by setting up the following equation
[
∑
i
=
0
r

c
1
i

C
i
]

[
1
c
2
c
2
2
⋮
]
=
0
with values of the matrices Ci's obtained from the two equations produced in step (a),
(c) obtaining all the real-valued roots, c1,real, of the parameters c1 to satisfy the equation

∑
i
=
0
r

c
1
i

C
i

=
0
which results from the equation produced in step (b),
(d) producing a list of real-valued pairs (c1,real, C2,real) by putting a value c1,real obtained in step (c) into the two equations produced in step (a) and obtaining the common real-valued c2,real of the two equations,
(e) obtaining the pair of (c1,real, c2,real) that gives ƒ(c1, c2) the minimal value by putting all sets of real-valued parameters into ƒ(c1, c2) and comparing their values.

145 more elements

Dependencies are inferred from the claim text.

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Abstract