Design and Implementation of High-Speed All-Pass Transformation-Based Variable Digital Filters by Breaking the Dependence of Operating Frequency on Filter Order

All-pass transformation (APT)-based variable digital filters (VDFs), also known as frequency warped VDFs, are typically used in various audio signal-processing applications. In an APT-based VDF, all-pass filter structures of appropriate order are used to replace the delay elements in a prototype filter structure. The resultant filter can provide variable frequency responses with unabridged control over cutoff frequencies on the fly, without updating the filter coefficients. In this brief, we briefly review the first- and second-order APT-based VDFs along with their hardware implementation architectures, and provide generalized design procedures to realize them as per required specifications. We also propose the modified pipelined hardware implementation architectures for both the first- and second-order APT-based VDFs. Field-programmable gate array implementation results of different first- and second-order APT-based VDF designs for both nonpipelined and pipelined implementation architectures are presented. An analysis of the results shows that the proposed pipelined implementation architectures result in high-speed VDFs, achieving high operating frequencies that are independent of the prototype filter order, for both the first- and second-order APT-based VDF designs.