Modes characterize resonant systems; estimating them accurately is tricky. Each mode of a system has a unique complex amplitude, a damping factor and a frequency. This toolbox contains algorithms to find modes from audio signals. Methods included are
- Frequency Zoomed-ARMA
- Frequency Zoomed-ESPRIT
- Frequency Warped-ESPRIT
Frequency-warped ESPRIT helps in estimating beating modes in the low frequency spectrum. Subband ESPRIT or frequency-zoomed ESPRIT replaces warping with bandwise filtering and downsampling, but is slower than FW-ESPRIT. FZ-ESPRIT is very similar to FZ-ARMA in spirit, but replaces ARMA modeling with ESPRIT, which is more robust. I'd recommend using FZ-ESPRIT when a large number of modes need to be estimated, such as in room impulse responses.
Time-domain sequential optimization, or frequency-domain constrained pole optimization further tunes the estimated modal parameters. The constrained pole optimizer has not been tested yet.
See example.m for an example on how to use the toolbox.
- Das, Orchisama and Jonathan S. Abel. "Modal Estimation on a Warped Frequency Axis for Linear System Modeling." arXiv Preprint, 2022 http://arxiv.org/abs/2202.11192.
- Karjalainen, Matti, Paulo AA Esquef, Poju Antsalo, Aki Mäkivirta, and Vesa Välimäki. "Frequency-zooming ARMA modeling of resonant and reverberant systems." Journal of the Audio Engineering Society 50, no. 12 (2002): 1012-1029.
- Kereliuk, Corey, Woody Herman, Russel Wedelich, and Daniel J. Gillespie. "Modal analysis of room impulse responses using subband ESPRIT." In Proceedings of the International Conference on Digital Audio Effects. 2018.
- Maestre, Esteban, Jonathan S. Abel, Julius O. Smith, and Gary P. Scavone. "Constrained pole optimization for modal reverberation." In Proc. of the 5th International Conference on Digital Audio Effects (DAFx). 2017.