Adaptive filter, step size control method thereof, and...

Details Adaptive filter, step size control method thereof, and... Adaptive filter, step size control method thereof, and...

1998-06-10

2001-04-24

Malzahn, David H. (Department: 2121)

Electrical computers: arithmetic processing and calculating

Electrical digital calculating computer

Particular function performed

Reexamination Certificate

active

06223194

ABSTRACT:

BACKGROUND OF THE INVENTION
The present invention relates to adaptive filters for identifying unknown systems, which are used as echo cancelers in audio systems, automatic equalizers for digital data transmission, etc.
DESCRIPTION OF THE PRIOR ART
At the outset, the principle behind conventional adaptive filters will be explained.
FIG. 1
is a block diagram showing a circuit in which an adaptive filter is used for identifying an unknown system.
The circuit of
FIG. 1
includes an adaptive filter
42
to which an input signal sequence is supplied and from which an estimate signal sequence is outputted, an unknown system
45
to which the same input signal sequence is supplied and from which an unknown signal sequence is outputted as the response to the input signal sequence, an adder
44
for adding additive noise to the unknown signal sequence outputted from the unknown system
45
, a subtracter
43
for subtracting the estimate signal sequence from the output of the adder
44
, and thereby outputting a signal sequence which is composed of an error signal sequence (between the unknown signal sequence and the estimate signal sequence) and the additive noise added together, to the adaptive filter
42
.
The adaptive filter
42
is a filter used for identifying the unknown system
45
, by generating the estimate signal sequence (an estimate of the response of the unknown system
45
to the input signal sequence) using the input signal sequence and by updating its filter parameters based on the error signal sequence (i.e. the difference between the unknown signal sequence and the estimate signal sequence). Usually, the additive noise is added to the unknown signal sequence as noise while observation.
As shown above, starting from an initial state in which the adaptive filter
42
has learned nothing, the adaptive filter
42
and its filter parameters converge on a particular final state, thereby identification of the unknown system
45
is performed.
In many cases, the same input signal sequence is supplied to both the unknown system
45
and the adaptive filter
42
as shown in FIG.
1
and the unknown signal sequence is given as the response of the unknown system
45
to the input signal sequence. Such principle is applied to echo cancelers, automatic equalizers, etc.
Next, detailed composition of the adaptive filter
42
shown in
FIG. 1
will be described referring to FIG.
2
.
FIG. 2
is a block diagram showing an example of composition of part of an adaptive filter. The circuit of
FIG. 2
includes a delay unit
51
for delaying the input signal sequence by a fixed time interval, a delay unit
52
for delaying each component a
n−k
of the delayed input signal sequence supplied from the delay unit
51
by a fixed time interval, a sign detector
54
for detecting the sign (i.e. polarity) of the sum of a component e
n
of the error signal sequence and a component &ugr;
n
of the additive noise sequence which are supplied thereto, a multiplier
55
for obtaining the product of the component a
n−k
and sgn(e
n
+&ugr;
n
) (Here, the component a
n−k
is a component of the delayed input signal sequence which is supplied from the delay unit
51
, and the sgn(e
n
+&ugr;
n
) is the sign of the sum of the error signal sequence component e
n
and the additive noise sequence component &ugr;
n
which are supplied from the sign detector
54
.), a multiplier
56
for multiplying the product outputted by the multiplier
55
by a step size &agr;
c
(n)
at time n, an adder
57
for adding the step size &agr;
c
(n)
at the time n (when the multiplication of the &agr;
c
(n)
was executed) and the k-th tap weight c
k
(n)
at the time n, and outputting the sum as the k-th tap weight c
k
(n+1)
at time n+1, a delay unit
53
for delaying the k-th tap weight c
k
(n+1)
at the time n+1 by a fixed time interval and thereby outputting the k-th tap weight c
k
(n)
at the time n, and a multiplier
58
for obtaining the product of the k-th tap weight c
k
(n)
and the delayed input signal sequence component a
n−k
supplied from the delay unit
51
.
An adaptive filter is usually realized as an FIR (Finite Impulse Response) filter (i.e. non-recursive filter) as shown in FIG.
2
. The
FIG. 2
is showing a circuit for controlling the k-th tap weight c
k
(n)
which is included in a set of N pieces of tap weights: {c
0
(n)
, c
1
(n)
, . . . , c
N−1
(n)
}. The resultant output obtained by the adaptive filter is the sum of outputs of such circuits corresponding to each k.
The N pieces of tap weights {c
0
(n)
, c
1
(n)
, . . . , c
N−1
(n)
} are controlled by the adaptive filter using the sum of the error signal sequence component e
n
and the additive noise sequence component &ugr;
n
. As mentioned above, in
FIG. 2
, n denotes time, a
n
denotes a component of the input signal sequence at the time n, and &agr;
c
(n)
denotes a step size at the time n. The tap weight control algorithm employed in the circuit of
FIG. 2
is stochastic gradient sign algorithm which is expressed as the following equation:
c
(n+1)
=c
(n)
+&agr;
c
(n)
sgn(e
n
+&ugr;
n
)a
(n)
where
c
(n)
=[c
0
(n)
,c
1
(n)
, . . . , c
N−1
(n)
]
T
and
a
(n)
=[a
n
,a
n−1
, . . . , a
n−N+1
]
T
.
Here, the c
(n)
and the a
(n)
in the above equations are the tap weights and the input signal sequence which are represented in the form of vectors. Incidentally, in the above equations, the ‘sgn( )’ represents the sign (i.e. the polarity) of ( ), and the ‘[ ]
T
’ represents the matrix transpose of [ ].
FIG. 3
is a block diagram showing another example of an adaptive filter. Similarly to
FIG. 2
,
FIG. 3
is showing a circuit for controlling the k-th tap weight c
k
(n)
, and the resultant output which is obtained by the adaptive filter is the sum of outputs of such circuits corresponding to each k. The N pieces of tap weights {c
0
(n)
, c
1
(n)
, . . . , c
N−1
(n)
} are controlled by the adaptive filter using the (e
n
+&ugr;
n
) in FIG.
3
. As mentioned above, n is denoting time, a
n
is denoting a component of the input signal sequence at the time n, and &agr;
c
(n)
is denoting a step size at the time n. The control algorithm for tap weights shown in
FIG. 3
is stochastic gradient algorithm which can be expressed more generally as the following equation:
c
(n+1)
=c
(n)
+&agr;
c
(n)
f(e
n
+&ugr;
n
)g(a
(n)
)
where
c
(n)
=[c
0
(n)
,c
1
(n)
, . . . , c
N−1
(n)
]
T
and
a
(n)
=[a
n
,a
n−1
, . . . , a
n−N+1
]
T
and
g(a
(n)
)=[g(a
n
),g(a
n−1
), . . . , g(a
n−N+1
)]
T
.
Here, both of the functions ‘f( )’ and ‘g( )’ are odd functions, and normally, nonlinear functions.
The following algorithms are industrially used as tap weight control algorithms of adaptive filters.
a. stochastic gradient LMS algorithm:
f(x)=x, g(a
(n)
)=a
(n)
b. stochastic gradient normalized LMS algorithm:
f(x)=x, g(a
(n)
)=a
(n)
/Pa, Pa=a
(n)T
a
(n)
c. stochastic gradient signed regressor algorithm:
f(x)=x, g(a
(n)
)=sgn(a
(n)
)
d. stochastic gradient sign algorithm (FIG.
2
):
f(x)=sgn(x), g(a
(n)
)=a
(n)
e. stochastic gradient sign-sign algorithm:
f(x)=sgn(x), g(a
(n)
)=sgn(a
(n)
)
For example, in the case of the stochastic gradient LMS algorithm (f(e
n
+&ugr;
n
)=e
n
+&ugr;
n
, g(a
(n)
)=a
(n)
), a circuit shown in
FIG. 4
can be adopted for controlling the k-th tap weight c
k
(n)
.
In the following, the setting of the step size &agr;
c
(n)
will be discussed. In the case where the step size &agr;
c
(n)
is a predetermined fixed value &agr;
cfixed
independently of the time n, convergence of the adaptive filter can be made faster by setting the fixed step size &agr;
cfixed
larger, as long as the fixed step size &agr;
cfixed
is in a range where the adaptive filter is stabl

Affiliated with

Also associated with

Rating

Adaptive filter, step size control method thereof, and... does not yet have a rating. At this time, there are no reviews or comments for this patent.

If you have personal experience with Adaptive filter, step size control method thereof, and..., we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and Adaptive filter, step size control method thereof, and... will most certainly appreciate the feedback.

Rate now

Comments { 0 }

Profile ID: LFUS-PAI-O-2445375