Nonlinear Phase FIR Filter Design according to the L 2 Norm with Constraints for the Complex Error (1994)
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BibTeX
@MISC{Lang94nonlinearphase,
author = {Markus Lang},
title = {Nonlinear Phase FIR Filter Design according to the L 2 Norm with Constraints for the Complex Error},
year = {1994}
}
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Abstract
We examine the problem of approximating a complex frequency response by a real-valued FIR filter according to the L 2 norm subject to additional inequality constraints for the complex error function. Starting with the Kuhn-Tucker optimality conditions which specialize to a system of nonlinear equations we deduce an iterative algorithm. These equations are solved by Newton's method in every iteration step. The algorithm allows arbitrary tradeoffs between an L 2 and an L1 design. The L 2 and the L1 solution result as special cases. Wir untersuchen das Problem der Approximation eines komplexen Frequenzganges mittels eines reellwertigen nichtrekursiven Filters nach der L 2 -Norm mit zusatzlichen Ungleichungsbedingungen fur die komplexe Fehlerfunktion. Ausgehend von den Kuhn-Tucker Optimalitatsbedingungen, die auf ein nichtlineares Gleichungssystem fuhren, leiten wir einen iterativen Algorithmus her. Diese Gleichungen werden in jedem Iterationsschritt mittels des Newton-Verfahrens gelost. D...
