Allpass Feedback Delay Networks

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

Connections between parallel and serial combinations of comb filters and feedback delay networks

Comb filters composed in a parallel or a serial way are a popular part of delay-line based artificial reverberators. Because the analysis of a complex comb filter structure can be tedious, there is a need for transforming such a structure into a compact and general representation. For this a transformation into the feedback delay network (FDN) filter structure is proposed as it is a general and well established framework to investigate the acoustic properties of the filter and therefore allows to compare different approaches