Wyniki wyszukiwania - BazTech

1

Stability Conditions for the Leaky LMS Algorithm Based on Control Theory Analysis

Bismor D., Pawelczyk M.

Archives of Acoustics

|

2016

|

Vol. 41, No. 4

731--739

EN

The Least Mean Square (LMS) algorithm and its variants are currently the most frequently used adaptation algorithms; therefore, it is desirable to understand them thoroughly from both theoretical and practical points of view. One of the main aspects studied in the literature is the influence of the step size on stability or convergence of LMS-based algorithms. Different publications provide different stability upper bounds, but a lower bound is always set to zero. However, they are mostly based on statistical analysis. In this paper we show, by means of control theoretic analysis confirmed by simulations, that for the leaky LMS algorithm, a small negative step size is allowed. Moreover, the control theoretic approach alows to minimize the number of assumptions necessary to prove the new condition. Thus, although a positive step size is fully justified for practical applications since it reduces the mean-square error, knowledge about an allowed small negative step size is important from a cognitive point of view.

2

LMS Algorithm Step Size Adjustment for Fast Convergence

Bismor D.

Archives of Acoustics

|

2012

|

Vol. 37, No. 1

31-40

EN

In the areas of acoustic research or applications that deal with not-precisely-known or variable condi- tions, a method of adaptation to the uncertainness or changes is usually necessary. When searching for an adaptation algorithm, it is hard to overlook the least mean squares (LMS) algorithm. Its simplicity, speed of computation, and robustness has won it a wide area of applications: from telecommunication, through acoustics and vibration, to seismology. The algorithm, however, still lacks a full theoretical analysis. This is probabely the cause of its main drawback: the need of a careful choice of the step size – which is the reason why so many variable step size flavors of the LMS algorithm has been developed. This paper contributes to both the above mentioned characteristics of the LMS algorithm. First, it shows a derivation of a new necessary condition for the LMS algorithm convergence. The condition, although weak, proved useful in developing a new variable step size LMS algorithm which appeared to be quite different from the algorithms known from the literature. Moreover, the algorithm proved to be effective in both simulations and laboratory experiments, covering two possible applications: adaptive line enhancement and active noise control.

3

Generation of effect of virtual undirectional source of sound using adaptive techniques

Bismor D.

Archives of Control Sciences

|

2003

|

Vol. 13, no. 2

215-230

EN

One of the main differences between standard industrial automation plants and acoustic plants is the presense of acoustic feedback between the contol value ("active" loudspeaker output) and measured disturbance value (reference microphone) [5]. There are reference sensor or feedback neutralization. This paper presents the author's experience with another approach to the problem, namely virtual unidirectional source of sound [13].