In which I think about parameterisations and implementations of audio recurrence for use in music.
A particular nook in the the linear feedback process library.
Designing stable delays
Also, parameterising stable Multi-Input-Multi-Output (MIMO) in signal processing can be done by using a Orthogonal and unitary matrices as the transfer operator.
Designing allpass delays
Keywords: multichannel allpass filter, MIMO allpass.
Designing delay lengths
Delays for signal interpolations
Things to try
- Gerzon m-dimensional MIMO unitary allpass
- Discuss what complex MIMO matrices would mean in this context
De Sena, Enzo, Huseyin Haciihabiboglu, Zoran Cvetkovic, and Julius O. Smith. 2015. “Efficient Synthesis of Room Acoustics via Scattering Delay Networks.” IEEE/ACM Transactions on Audio, Speech, and Language Processing 23 (9): 1478–92. https://doi.org/10.1109/TASLP.2015.2438547.
Menzer, Fritz, and Christof Faller. 2010. “Unitary Matrix Design for Diffuse Jot Reverberators.” https://www.researchgate.net/publication/230757792_Unitary_Matrix_Design_for_Diffuse_Jot_Reverberators.
Regalia, P., and M. Sanjit. 1989. “Kronecker Products, Unitary Matrices and Signal Processing Applications.” SIAM Review 31 (4): 586–613. https://doi.org/10.1137/1031127.
Schroeder, Manfred R. 1961. “Improved Quasi-Stereophony and ‘Colorless’ Artificial Reverberation.” The Journal of the Acoustical Society of America 33 (8): 1061–4. https://doi.org/10.1121/1.1908892.
Schroeder, Manfred R., and B. Logan. 1961. “"Colorless" Artificial Reverberation.” Audio, IRE Transactions on AU-9 (6): 209–14. https://doi.org/10.1109/TAU.1961.1166351.
Tilma, Todd, and E C G Sudarshan. 2002. “Generalized Euler Angle Paramterization for SU(N).” Journal of Physics A: Mathematical and General 35 (48): 10467–10501. https://doi.org/10.1088/0305-4470/35/48/316.
Valimaki, v., and T. I. Laakso. 2012. “Fractional Delay Filters-Design and Applications.” In Nonuniform Sampling: Theory and Practice, edited by Farokh Marvasti. Springer Science & Business Media. http://books.google.com?id=n3fgBwAAQBAJ.