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.
Weapons of choice:
- Parameterisations of sparse unitary matrices
Keywords: multichannel allpass filter.
One obvious parameterisation of unitary matrices is applying givens rotations to the identity matrix; this has parameters.
Note that the recurrent neural networks people have glommed on to this. (ArSB15, MHRB16, JSDP16)
Things to try
- Generalise reverb to Gerzon m-dimensional MIMO unitary allpass
- Thiran (multi-step, SISO) allpass?
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- MHRB17: (2017) Efficient Orthogonal Parametrisation of Recurrent Neural Networks Using Householder Reflections. In PMLR (pp. 2401–2409).
- DHCS15: (2015) Efficient Synthesis of Room Acoustics via Scattering Delay Networks. IEEE/ACM Transactions on Audio, Speech, and Language Processing, 23(9), 1478–1492. DOI
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- JSDP17: (2017) Tunable Efficient Unitary Neural Networks (EUNN) and their application to RNNs. In PMLR (pp. 1733–1741).
- ArSB16: (2016) Unitary Evolution Recurrent Neural Networks. In Proceedings of the 33rd International Conference on International Conference on Machine Learning - Volume 48 (pp. 1120–1128). New York, NY, USA: JMLR.org
- MeFa10: (2010) Unitary Matrix Design for Diffuse Jot Reverberators.