Improved bi-equiripple variable fractional-delay filters

• Published in: Signal processing Vol. 94; pp. 300 - 307
• Main Authors: Deng, Tian-Bo, Qin, Wei
• Format: Journal Article
• Language: English
• Published: Amsterdam Elsevier B.V 01.01.2014; Elsevier
• Subjects: Applied sciences; Bi-equiripple; Detection, estimation, filtering, equalization, prediction; Digital filters; Error functions; Errors; Exact sciences and technology; Flattening; Frequency response; Information, signal and communications theory; Minimax technique; Second-order-cone (SOC) constraint; Signal and communications theory; Signal processing; Signal, noise; Telecommunications and information theory; Variable fractional-delay (VFD); Variable frequency response (VFR); Variable frequency response (VFR); Variable fractional-delay (VFD); Bi-equiripple; Second-order-cone (SOC) constraint; Performance evaluation; Second order; Error function; Iterative method; Linear programming; Digital filter; Minimax method; Signal processing; Finite impulse response filter; Frequency response; Delay time
• ISSN: 0165-1684; 1872-7557
• DOI: 10.1016/j.sigpro.2013.07.004

This paper presents a bi-minimax method for designing an odd-order variable fractional-delay (VFD) finite-impulse-response (FIR) digital filter such that both the peak errors of its variable frequency response (VFR) and VFD response can be simultaneously suppressed. The bi-minimax design iteratively minimizes a mixed error function involving both the VFR-peak-error and VFD-peak-error subject to the second-order-cone (SOC) constraints on the VFR errors and linear-programming (LP) constraints on the VFD errors. As compared with the existing SOC-based minimax design that minimizes the VFR-peak-error only, this odd-order bi-minimax design suppresses the VFD-peak-error and flattens both the VFR errors and VFD errors simultaneously. Consequently, both the two errors are made nearly equi-ripple (bi-equiripple). An example is given for showing the simultaneous suppression of the two kinds of peak errors and verifying the effectiveness of the odd-order bi-minimax design approach. •We propose an improved method for designing bi-equiripple VFD filters.•This bi-minimax design suppresses both VFD-peak-error and VFR-peak error.•An alternating optimization approach is applied.•An example is given for illustrating the performance improvement.