Generalized WLS Method for Designing Allpass Variable Fractional-Delay Digita...

caroline11

Abstract— This paper presents an optimal weighted-leastsquares (WLS) method for designing low-complexity allpass variable fractional-delay (VFD) digital filters. Instead of using a fixed range for the VFD parameter p and same-order constantcoefficient filters (subfilters), both the VFD parameter range p ∈ [pMin, pMax] and subfilter orders are optimized such that a low-complexity allpass VFD filter can be achieved for the leastsquares (LS) design. To suppress the peak errors of variable frequency response, weighting functions are adopted and optimized such that the boundary peak errors can be further reduced but without noticeably increasing the total error energy (integral of squared error) of variable frequency response. After optimizing the variable range of the VFD parameter, weighting functions, and subfilter orders, an allpass VFD filter can be designed by using a generalized noniterative WLS method, which yields a closed-form solution. Design examples are given to illustrate that utilizing different-order subfilters along with the optimal range and optimal weighting functions can yield an allpass VFD filter with signifiantly reduced complexity and design errors as compared with the existing ones.