Colloquia, Seminars and Conference News
Title : Adaptive Digital Filtering Algorithms: Theory and Applications
Date : April 21, 2008. (2:00 pm) Tea starts half an hour before each seminar
Location: ITEB 336
Speaker : Prof. Elsayed Abdel Aziz Soleit
Abstract:
The adaptive filtering theory is based on the Wiener optimal filtering theory that depends on minimizing of an objective function or a performance criterion. The well-known performance criteria are the mean square error (MSE) and the recursive least square (RLS) error criteria. The error signal is created by subtracting the filter output from a desired (target) output or response. The filter output is defined by using the linear convolution theory which convolves the input observations with the filter impulse response. Generally, the filter impulse response is not known and it is required to be designed optimally. Hence, the adaptive digital filter is configured either a finite impulse response (FIR) (non-recursive) or an infinite impulse response (IIR) structure. The filter response is calculated in terms of the filter coefficients and the input observation vectors. Thus, the MSE performance criterion is considered a quadratic function of the coefficient vector and behaves as unimodal surface that includes a global optimum solution. Wiener and Hopf have derived that the global optimal solution is equivalent to the multiplication of the inverse of the autocorrelation matrix of the input observations by the cross-correlation vector of the desired output and the input observation vector.
However, the direct solution of the Wiener-Hopf equation requires the calculation of the second order statistics of the input sequences which are unknown in various applications. Also, it is not preferred in the real time applications.
The adaptation algorithms are introduced to solve the Wiener-Hopf equation iteratively such that a certain performance criterion is minimized. The weight coefficient vector converges to the optimal solution after a convergence time. A lot of adaptation algorithms are introduced and modified according to the applications. The well-known adaptation algorithms based on the gradient technique are the least mean square (LMS) that is derived by Widrow and the recursive least square (RLS) to update the weight coefficients of the FIR filter. Several improvements of the LMS and the RLS algorithms are proposed by many authors to update the weight coefficients of the FIR and IIR filters.
The adaptive digital filter comprises of two main modules; the convolution module and the adaptation algorithm one. The convolution module is responsible to compute the filter output and the adaptation algorithm module is to update the filter coefficients such that the assigned performance criterion is minimized. The performance measure of the adaptive filter is outlined as: the convergence rate (adaptation speed), mis-adjustment (adaptation noise), the system stability, the tracking speed, the computation requirements and the structure complexity. The main applications of the adaptive filtering technique that will be handled in the talk are as follows:
• System modeling and Identification
• Inverse modeling and channel equalization
• Interference and noise cancellation
• Path tracking and control
• Image processing and pattern recognition
• Speech processing and recognition
• Image compression
Bio:
[Back]
