TY - JOUR
T1 - Allpass Feedback Delay Networks
AU - Schlecht, Sebastian J.
PY - 2021/1/21
Y1 - 2021/1/21
N2 - 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.
AB - 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.
KW - Allpass Filter
KW - Delay lines
KW - Delay State Space
KW - Delays
KW - Feedback Delay Networks
KW - Filter Design
KW - Jacobian matrices
KW - MIMO
KW - MIMO communication
KW - SISO
KW - Stability criteria
KW - Symmetric matrices
KW - Transfer functions
UR - http://www.scopus.com/inward/record.url?scp=85100448881&partnerID=8YFLogxK
U2 - 10.1109/TSP.2021.3053507
DO - 10.1109/TSP.2021.3053507
M3 - Article
AN - SCOPUS:85100448881
SN - 1053-587X
VL - 69
SP - 1028
EP - 1038
JO - IEEE Transactions on Signal Processing
JF - IEEE Transactions on Signal Processing
M1 - 9332286
ER -