Allpass VFD Filter Design

• Published in: IEEE transactions on signal processing Vol. 58; no. 8; pp. 4432 - 4436
• Main Authors: Dam, Hai Huyen, Teo, Kok Lay
• Format: Journal Article
• Language: English
• Published: New York, NY IEEE 01.08.2010; Institute of Electrical and Electronics Engineers; The Institute of Electrical and Electronics Engineers, Inc. (IEEE)
• Subjects: Algorithms; Allpass filter design; Applied sciences; Approximation; Constraint optimization; Cost function; Delay effects; Delay estimation; Detection, estimation, filtering, equalization, prediction; Deviation; Digital filters; Errors; Exact sciences and technology; filled function; Finite impulse response filter; Inequalities; Inequality; Information, signal and communications theory; Integrals; Least squares approximation; Miscellaneous; Nonlinearity; Optimization; Optimization methods; Signal and communications theory; Signal processing; Signal, noise; Smoothing methods; Stability; Studies; Telecommunications and information theory; variable digital filter design; Global optimum; Nonlinear problems; Optimization; All pass filter; Penalty function; Allpass filter design; Digital filter; filled function; variable digital filter design; Weight function; Signal processing; Cost function; Delay time
• ISSN: 1053-587X; 1941-0476
• DOI: 10.1109/TSP.2010.2048316

This correspondence proposes a general design for allpass variable fractional delay (VFD) digital filters with minimum weighted integral squared error subject to constraints on maximum error deviation from the desired response. The resulting optimization problem is nonlinear and nonconvex with a nonlinear continuous inequality constraint. Stability of the designed filters are discussed. An effective procedure is proposed for solving the optimization problem. Firstly, a constraint transcription method and a smoothing technique are employed to transform the continuous inequality constraint into one equality constraint. Then, by using the concept of a penalty function, the transformed constraint is incorporated into the cost function to form a new cost function. The nonlinear optimization problem subject to continuous inequality constraints is then approximated by a sequence of unconstraint optimization problems. Finally, a global optimization method using a filled function is employed to solve the unconstraint optimization problem. Design example shows that a trade-off can be achieved between the integral squared error and the maximum error deviation for the design of allpass VFD filters.