Improved bi-equiripple variable fractional-delay filters

• 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.

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.