Abstract
In the 1960s, Schroeder and Logan introduced delay line-based allpass filters, which are still popular due to their computational efficiency and versatile applicability in artificial reverberation, decorrelation, and dispersive system design. In this work, we extend the theory of allpass systems to any arbitrary connection of delay lines, namely feedback delay networks (FDNs). We present a characterization of uniallpass FDNs, i.e., FDNs, which are allpass for an arbitrary choice of delays. Further, we develop a solution to the completion problem, i.e., given an FDN feedback matrix to determine the remaining gain parameters such that the FDN is allpass. Particularly useful for the completion problem are feedback matrices, which yield a homogeneous decay of all system modes. Finally, we apply the uniallpass characterization to previous FDN designs, namely, Schroeder's series allpass and Gardner's nested allpass for single-input, single-output systems, and, Poletti's unitary reverberator for multi-input, multi-output systems and demonstrate the significant extension of the design space.
Highlights
A LLPASS filters preserve the signal’s energy and only alter the signal phase [1]
SISO allpass feedback delay networks (FDNs) can be composed from simple allpass filters in series [2], [12] or by nesting [13]
We extend the theory of allpass FDNs for both SISO and MIMO
Summary
A LLPASS filters preserve the signal’s energy and only alter the signal phase [1]. Schroeder and Logan generalized the first-order allpass filter replacing the single delay with a delay line [2]. MIMO allpass filters can be generated from simple unitary building blocks [4], [14] or by generalizing the allpass lattice structure [15] Both SISO and MIMO allpass FDNs were applied to a wide range of roles including: 1) increasing the echo density as Manuscript received July 8, 2020; revised December 23, 2020 and January 14, 2021; accepted January 16, 2021. It is often desirable to first design the feedback matrix and subsequently choose the input, output, and direct gains such that the resulting FDN is allpass We refer to this procedure as the completion problem. This work extends the design space of delay line-based allpass filters from a handful of known structures to a freely parametrizable extensive class. A MATLAB implementation of all plots, examples and the completion algorithm are included in the FDN toolbox [37].2
Sign-in/Register to view highlights & summary Sign-in/Register to access full text options 
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a callDisclaimer: All third-party content on this website/platform is and will remain the property of their respective owners and is provided on "as is" basis without any warranties, express or implied. Use of third-party content does not indicate any affiliation, sponsorship with or endorsement by them. Any references to third-party content is to identify the corresponding services and shall be considered fair use under The CopyrightLaw.
