Lyapunov-style proof of stability of quantized-error algorithm contrasts with averaging results for quantized-regressor algorithm. Helps to determine which algorithm is most appropriate in a given application.
W. A. Sethares and C. R. Johnson, Jr., "A Comparison of Two Quantized State Adaptive Algorithms," IEEE Trans. on Acoustics, Speech, and Signal Processing, Vol. 37, No. 1, pp. 138-143, Jan. 1989.
Averaging applied to the Constant Modulus Algorithm; gives first theoretical demonstration of when and why this algorithm "works."
C. R. Johnson, Jr., S. Dasgupta, and W. A. Sethares, "Averaging Theory for Proof of Local Stability of Real CMA," IEEE Trans. on Acoustics, Speech, and Signal Processing, Vol. 36, No. 6, pp. 900-910, June 1988.
Signed IIR algorithms explored in terms of a geometric criterion. Raises important general questions for communication standards such as ADPCM.
C. R. Elevitch, W. A. Sethares, and C. R. Johnson, Jr., "Quiver Diagrams for Signed Adaptive Algorithms," IEEE Trans. on Acoustics, Speech, and Signal Processing, Vol. 37, No. 2, pp. 227-235, Feb. 1989.
This study amalgamates virtually all known adaptive algorithms (with linear filters on error and regressor) into a simple generic form. Uses averaging theory to derive concrete expressions for behavior, especially stability.
W. A. Sethares, B. D. O. Anderson, C. R. Johnson, Jr., "Adaptive Algorithms with Filtered Regressor and Filtered Error," Mathematics of Control, Signals, and Systems, 2:381-403, 1989.
This book chapter summarizes the three major ways that people analyze adaptive algorithms (the expected value, deterministic averaging, and ODE approaches), and contains applications in several signal processing areas.
W. A. Sethares, The LMS Family, in Efficient System Identification and Signal Processing Algorithms, Ed. N. Kalouptsidis and S. Theodoridis, Springer-Verlag, 1993.
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