Patent Application
20080095389
The following detailed description of the present invention refers to subject matter in the accompanying drawings which show, by way of illustration, specific aspects and embodiments in which the present subject matter may be practiced. These embodiments are described in sufficient detail to enable those skilled in the art to practice the present subject matter. References to “an”, “one”, or “various” embodiments in this disclosure are not necessarily to the same embodiment, and such references contemplate more than one embodiment. The following detailed description is, therefore, not to be taken in a limiting sense, and the scope is defined only by the appended claims, along with the full scope of legal equivalents to which such claims are entitled.
The present system may be employed in a variety of hardware devices, including hearing assistance devices. Such devices may include a signal processor or other processing hardware to perform functions. One such function is acoustic feedback cancellation using an adaptive filter. In such embodiments, the acoustic feedback cancellation filter models the acoustic feedback path from receiver to microphone of the hearing assistance system to subtract the acoustic feedback that occurs without such correction. In one embodiment, entrainment is avoided by using signal processing electronics to determine the denominator of the system transfer function and analyze the denominator of the system transfer function for stability. If the position of the poles indicate entrainment, the processor determines and implements a change to the adaptation rate of the system.
In general, the present subject matter achieves entrainment avoidance by transforming the denominator of the system transfer function to lattice form and monitoring the reflection coefficients for indication of entrainment. Entrainment is probable where the reflection coefficients approach unity stability.
The feedback canceller system of equations can be transformed to control canonical form and apply the Lyapunov stability as shown below,
x
k+1
=Ax
k
+Bu
k
k=0, 1, 2, . . .
is determined using Lyapunov function, where A is the linear system matrix and x is the input matrix.
V(x)=xTQx,
where V(x) is the Lyapunov function. If the derivative, ΔV(x), is positive near the neighborhood of interest, the system is stable in that neighborhood. x denote the real vector of dimension n, A and Q are quadratic matrices. The derivative of V(x) with respect to time is give by
A
T
QA−Q=−S.
αi*αj≠1 and αi≠1 i=0, 1, 2, . . .
hold for all eigenvalues αi of A.
From the equations above, for a positive definite Q matrix, the eigenvalues of the system B are inside the unit circle of stability. It is known that the solution to discrete time Lyapunov function is the same as looking into a Schur polynomial solution in order reverse form.
The Schur-Cohn stability test has the property of being a recursive algorithm. This is a consequence of the simultaneously algebraic and analytic aspect of the Schur coefficients, which are regarded as reflection coefficients. The denominator polynomial is converted to lattice form with reflection coefficients using Schur polynomials. The reflection coefficient magnitudes are used to evaluate the stability of the system.
The lattice structures with reflection coefficients K1, K2 . . . Km correspond to a class of m direct-form FIR filters with system functions D1(z), D2(z), . . . Dm(z). Given the D(z) matrix, the corresponding lattice filter parameters {Km} are determined. For the m stage lattice system, the initial parameter Km=dm. Km-1 is obtained from the polynomials Dm-1(z) since Km is obtained from the polynomial Dm(z) for m=M−1, M−2, . . . , 1. The lattice filter parameters Km's are computed recursively starting from m=M−1 to m=1 as,
The above recursion is known as the Schur-Cohen stability test. In doing that we compute the lower degree polynomials. The procedure works as long as Km 6=1 for m=1, 2, . . . , (M−1). Let denominator polynomials be D(z),
D(z)=1−G(z)(F0(z)−W(z)),
where k is the system delay and M is the number of taps of the feedback canceller.
If poles move outside the unit circle due to instability a new frequency is created. In order to avoid the poles reaching unit circle or stability boundary, In various embodiments, a pseudo unit circle, which is smaller than unit circle, is used for analyzing the stability. Prior to the analyzing the denominator polynomial, D(z) is scaled by a factor. The scaling the polynomial is with,
{tilde over (d)}
i
=d
i*ρi for i=0, 1, 2, . . . , (M+K−1),
where ρ>1 is a scaling factor which is chosen between 1.01 and 1.05 to arrive at the pseudo circle.
Entrainment avoidance is achieved using the signal processor to analyze the denominator polynomial for stability and changing the adaptation rate of the system depending on the position of the poles. The analysis algorithm includes stages to initialize the feedback canceller, generate future pole positions, analyze the stability of the future pole positions with respect to a pseudo stability circle and adjust the adaptation rate of the feedback canceller in light of the analysis.
Initializing the feedback controller establishes a good estimate of the feedback path, F0(z). A good estimate of the leakage path, F0(z) is necessary to generate the denominator polynomial, D(z). In various embodiments, a good estimate can be found by a forward gain module disconnected white noise initialization, where the system gets simplified to a system identification configuration. The is known to accurately estimate F0(z). In various embodiments, a good estimate of F0(z) is achieved by copying the Wn(z) coefficients to F0(z) at a point where the feedback canceller is modeling the feedback path. In order to identify a suitable time for copying the coefficients, the convergence accuracy can be analyzed by monitoring the average en values.
Once the denominator polynomial is constructed, the denominator is scaled by multiplications of the denominator as shown above. The scaled denominator is used to identify the pole position of the system at a future iteration.
In various embodiments, the future pole position is converted to Lattice form to evaluate stability. This can be viewed as comparing the poles against a pseudo unit circle described above. Use of the pseudo circle is important since once the poles of the system moves outside the stable region, regaining stability of the system is difficult.
In various embodiments, if the poles move outside the pseudo circle and a update of the filter coefficients is to take place, we stop adaptation by not updating the filter. In some situations if the adaptation is constantly trying to move out of the unit circle in a predictable manner it is possible to reverse the update. This can be viewed as a negative adaptation and can be useful in some situations. If adaptation is stopped for some random movement of a pole outside the circle as the pole returns the adaptation will continue to regain the stability.
By using the Schur polynomials the pole space is translated into the reflection coefficient space. This method is used in time-varying IIR filters. Lattice structure is used to ensure stability of the system without identifying the roots of a system transfer function. If one or more reflection coefficients are larger than one, the system is unstable. For electro-acoustic systems, it is reasonable to conclude that the entrainment is the main driving force of the poles outside the unit circle. An alternate method of combating entrainment includes reversing the adaptation process. This method does bring the system back to stability due to the stochastic nature of the NLMS algorithm, where stopping the system from adapting, reduces the ability of the system to recover from some adverse entrainment conditions.
The following complexity calculation is for comparison with the standards NLMS feedback canceller algorithm for the canceller path. Even though the algorithm is significantly more complex, the performance of this algorithm is similar to the standard NLMS algorithm when the system poles are inside the unit circle. Where M is the number of NLMS filter taps and D is length of the denominator polynomial which depends on the effective feedback leakage path (identified during the initialization phase). Assuming the denominator length to be same as the feedback canceller length for simplicity, the pole stabilizing algorithm totals to ˜6M complex and 7M simple operations. This is comparatively expensive than the ˜3M complex and 4M simple operations for standard NLMS feedback canceller algorithms. This algorithm can be decimated to reduce the complexity.
It is understood that the foregoing teachings may be employed in different hardware, firmware, or software configurations and combinations thereof. It is understood that the embodiments set forth herein may be employed in different devices, including, hearing assistance devices, such as hearing aids. Such hearing aids may include, but are not limited to, behind-the-ear, in-the-ear, and completely-in-the-canal designs. Other applications of the foregoing teachings are possible without departing from the scope of the present subject matter.
This application is intended to cover adaptations or variations of the present subject matter. It is to be understood that the above description is intended to be illustrative, and not restrictive. The scope of the present subject matter should be determined with reference to the appended claims, along with the full scope of equivalents to which such claims are entitled.
This application claims the benefit under 35 U.S.C. 119(e) of U.S. Provisional Patent Application Ser. No. 60/862,545, filed Oct. 23, 2006, the entire disclosure of which is hereby incorporated by reference in its entirety.
| Number | Date | Country | |
|---|---|---|---|
| 60862545 | Oct 2006 | US |
