Adaptive filter method, system and apparatus
AssigneeKing Fahd University of Petroleum and Minerals
InventorsAhmad KHALIFI, Azzedine Mohamed Ali ZERGUINE
Life of this patent
Estimating the term…
Abstract
The present disclosure relates to adaptive filtering optimization methods based on a hyperbolic sine cost function. While the adaptive filtering optimization methods belong to the variable step-size class, however, the present disclosure describes a new approach requiring tuning of only one parameter. The present disclosure is further related to a family of higher order hyperbolic sine cost functions.
Claims20
A method for adaptive filtering, the method comprising:
- receiving, via processing circuitry, an input signal;
- generating, via the processing circuitry, an initial output signal based upon an initial set of one or more coefficients;
- determining, via the processing circuitry, an error signal based upon the difference between the initial output signal and a desired response signal;
- calculating, via the processing circuitry, a solution to a function based upon the error signal;
- and
- generating, via the processing circuitry, a subsequent output signal based upon a subsequent set of one or more coefficients,
- wherein the subsequent set of one or more coefficients is determined by adjusting the initial set of one or more coefficients based upon the calculation of the solution to the function,
- wherein the initial set of one or more coefficients is adjusted in order to minimize the function,
- wherein the function is a hyperbolic sine-based function.
The method according to 1, wherein the function is a second order hyperbolic sine-based function.
The method according to 1, wherein the function is a fourth order hyperbolic sine-based function.
The method according to 1, wherein the function is defined as
- J
-
- (
- k
- )
- =
- 1
- A
-
- sinh
-
- (
- Ae
- 2
-
- (
- k
- )
- )
- ,
- where J is a value of the function, k is a time value, A is a tuning parameter, and e is the error signal.
The method according to 1, wherein the function is defined as
- J
-
- (
- k
- )
- =
- 1
- 4
-
- A
-
- sinh
-
- (
- Ae
- 2
-
- (
- k
- )
- )
- ,
- where J is a value of the function, k is a time value, A is a tuning parameter, and e is the error signal.
The method according to 1, wherein a stochastic gradient of the function comprises a time-varying step-size.
The method according to 6, wherein the stochastic gradient of the function further comprises an upper bound step-size and a lower bound step-size.
The method according to 6, wherein the stochastic gradient of the function further comprises a generic upper bound step-size.
The method according to 8, wherein the generic upper bound step-size is defined as
- μ
- m
-
-
- ax
- =
- 1
- Tr
-
- {
- R
- x
- }
- +
- ϵ
- ·
- 1
- 1
- +
- e
- 2
- ·
- (
- k
- )
- ,
- where Tr is a trace operator, Rx is an auto-correlation matrix of the input signal, ϵ is a non-zero constant, k is a time value, and e is the error signal.
The method according to 8, wherein the generic upper bound step-size is defined as
- μ
- m
-
-
- ax
- =
- 1
- Tr
-
- {
- R
- x
- }
- +
- ϵ
- ,
- where Tr is a trace operator, Rx is an auto-correlation matrix of the input signal, and ϵ is a non-zero constant.
A device for adaptive filtering, comprising a processing circuitry configured to:
- receive an input signal;
- generate an initial output signal based upon an initial set of one or more coefficients;
- determine an error signal based upon the difference between the initial output signal and a desired response signal;
- calculate a solution to a function based upon the error signal;
- and
- generate a subsequent output signal based upon a subsequent set of one or more coefficients,
- wherein the subsequent set of one or more coefficients is determined by adjusting the initial set of one or more coefficients based upon the calculation of the solution to the function,
- wherein the initial set of one or more coefficients is adjusted in order to minimize the function,
- wherein the function is a hyperbolic sine-based function.
The device according to 11, wherein the function is a second order hyperbolic sine-based function, a fourth order hyperbolic sine-based function, or a combination thereof.
The device according to 11, wherein the function is defined as
- J
-
- (
- k
- )
- =
- 1
- A
-
- sinh
-
- (
- Ae
- 2
-
- (
- k
- )
- )
- ,
- where J is a value of the function, k is a time value, A is a tuning parameter, and e is the error signal.
The device according to 11, wherein the function is defined as
- J
-
- (
- k
- )
- =
- 1
- 4
-
- A
-
- sinh
-
- (
- Ae
- 2
-
- (
- k
- )
- )
- ,
- where J is a value of the function, k is a time value, A is a tuning parameter, and e is the error signal.
The device according to 11, wherein a stochastic gradient of the function comprises a time-varying step-size.
The device according to 15, wherein the stochastic gradient of the function further comprises an upper bound step-size and a lower bound step-size.
The device according to 15, wherein the stochastic gradient of the function further comprises a generic upper bound step-size.
The device according to 17, wherein the generic upper bound step-size is defined as
- μ
- m
-
-
- ax
- =
- 1
- Tr
-
- {
- R
- x
- }
- +
- ϵ
- ·
- 1
- 1
- +
- e
- 2
- ·
- (
- k
- )
- ,
- where Tr is a trace operator, Rx is an auto-correlation matrix of the input signal, ϵ is a non-zero constant, k is a time value, and e is the error signal.
The device according to 17, wherein the generic upper bound step-size is defined as
- μ
- m
-
-
- ax
- =
- 1
- Tr
-
- {
- R
- x
- }
- +
- ϵ
- ,
- where Tr is a trace operator, Rx is an auto-correlation matrix of the input signal, and ϵ is a non-zero constant.
A non-transitory computer-readable medium comprising a set of instructions, which, when executed by a processing circuitry, cause the processing circuitry to perform a method for adaptive filtering, comprising:
- receiving, via processing circuitry, an input signal;
- generating, via the processing circuitry, an initial output signal based upon an initial set of one or more coefficients;
- determining, via the processing circuitry, an error signal based upon the difference between the initial output signal and a desired response signal;
- calculating, via the processing circuitry, a solution to a function based upon the error signal;
- and
- generating, via the processing circuitry, a subsequent output signal based upon a subsequent set of one or more coefficients,
- wherein the subsequent set of one or more coefficients is determined by adjusting the initial set of one or more coefficients based upon the calculation of the solution to the function,
- wherein the initial set of one or more coefficients is adjusted in order to minimize the function,
- wherein the function is a hyperbolic sine-based function.
Dependencies are inferred from the claim text.