The Living Thing / Notebooks :

Filter design, linear

especially digital

Linear Time-Invariant (LTI) filter design is a productive and satisfying sub-field of signal processing, and a special case state filtering that don’t necessarily involve a hidden state.

z-Transforms, bilinear transforms (blech!), Bode plots, design etc.

Contents

I am going to consider this in discrete time (i.e. for digital implementation) unless otherwise stated, because I’m implementing this in software, not with capacitors or whatever. For reasons of tradition we usually start from continuous time systems, but this is not necessarily a convenient mathematical or practical starting point for my own work.

This notebook is about designing properties of systems to given specifications, e.g. signal to noise ratios, uncertainty principles

For inference of filter parameters from data, you want system identification; and for working out the hidden states of the system given the parameters, you want the more general estimation theory in state filters.

Related, musical: delays and reverbs.

Relationship of discrete LTI to continuous time processes

TBD, based on the modern summary in Mart99. But I’m way more interested in representations of systems more naturally represented with delays, and those are easier in digital discrete time than RCL circuit design, so I can’t imagine racing to get to this.

Quick and dirty digital filter design

State-Variable Filters

A vacuous name; every recursive filter has state variables. Less ambiguous: Chamberlin and Zölzer filters.

Nigel Redmon, digital SVF intro.

Heavy-tailed noise

If your noise is heavy tailed, what works? I suspect this causes problems even if it is white noise, but haven’t looked into it. TBD.

Refs, sundry

AbKI95
Abe, T., Kobayashi, T., & Imai, S. (1995) Harmonics tracking and pitch extraction based on instantaneous frequency. In International Conference on Acoustics, Speech, and Signal Processing, 1995. ICASSP-95 (Vol. 1, pp. 756–759 vol.1). DOI.
Alli92
Alliney, S. (1992) Digital filters as absolute norm regularizers. IEEE Transactions on Signal Processing, 40(6), 1548–1562. DOI.
Anto05
Antoniou, A. (2005) Digital signal processing: signals, systems and filters. . New York: McGraw-Hill
BeZa76
Berkhout, A. J., & Zaanen, P. R.(1976) A Comparison Between Wiener Filtering, Kalman Filtering, and Deterministic Least Squares Estimation*. Geophysical Prospecting, 24(1), 141–197. DOI.
Cham85
Chamberlin, H. (1985) Musical applications of microprocessors. (2nd ed.). Hasbrouck Heights, N.J: Hayden Book Co.
HaLu14
Harvey, A., & Luati, A. (2014) Filtering With Heavy Tails. Journal of the American Statistical Association, 109(507), 1112–1122. DOI.
Hohm02
Hohmann, V. (2002) Frequency analysis and synthesis using a Gammatone filterbank. Acta Acustica United with Acustica, 88(3), 433–442.
Laro07a
Laroche, J. (2007a) On the Stability of Time-Varying Recursive Filters. Journal of the Audio Engineering Society, 55(6), 460–471.
Laro07b
Laroche, J. (2007b) On the Stability of Time-Varying Recursive Filters. Journal of the Audio Engineering Society, 55(6), 460–471.
Marp87
Marple, S. L., Jr. (1987) Digital spectral analysis with applications.
Mart98
Martin, R. J.(1998) Autoregression and irregular sampling: Filtering. Signal Processing, 69(3), 229–248. DOI.
Mart99
Martin, R. J.(1999) Autoregression and irregular sampling: Spectral estimation. Signal Processing, 77(2), 139–157. DOI.
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Moon, T. K., & Stirling, W. C.(2000) Mathematical methods and algorithms for signal processing. . Upper Saddle River, NJ: Prentice Hall
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Moorer, J. . (1974) The optimum comb method of pitch period analysis of continuous digitized speech. IEEE Transactions on Acoustics, Speech and Signal Processing, 22(5), 330–338. DOI.
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Narasimha, M. J., Ignjatovic, A., & Vaidyanathan, P. P.(2002) Chromatic derivative filter banks. IEEE Signal Processing Letters, 9(7), 215–216. DOI.
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Necciari, T., Balazs, P., Holighaus, N., & Sondergaard, P. L.(2013) The ERBlet transform: An auditory-based time-frequency representation with perfect reconstruction. In 2013 IEEE International Conference on Acoustics, Speech and Signal Processing (ICASSP) (pp. 498–502). DOI.
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Nyquist, H. (1928) Certain Topics in Telegraph Transmission Theory. Transactions of the American Institute of Electrical Engineers, 47(2), 617–644. DOI.
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Oppenheim, A. V., Schafer, R. W., & Buck, J. R.(1999) Discrete-time signal processing. (2nd ed.). Upper Saddle River, N.J: Prentice Hall
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Orfanidis, S. J.(1996) Introduction to signal processing. . Englewood Cliffs, N.J: Prentice Hall
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Prandoni, P., & Vetterli, M. (2008) Signal processing for communications. . Lausanne: EPFL Press
RoSP11
Robertson, A., Stark, A. M., & Plumbley, M. D.(2011) Real-Time Visual Beat Tracking Using a Comb Filter Matrix. In Proceedings of the International Computer Music Conference 2011.
Smit10
Smith III, J. O.(2010) Audio signal processing in Faust. Online Tutorial: Https://Ccrma. Stanford. Edu/Jos/Aspf.
Smit07
Smith, J. O.(2007) Introduction to Digital Filters with Audio Applications. . http://www.w3k.org/books/: W3K Publishing
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Smith, J. O., & Michon, R. (2011) Nonlinear allpass ladder filters in faust. In Proceedings of the 14th International Conference on Digital Audio Effects (DAFx-11) (pp. 361–364).
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Stoica, P., & Moses, R. L.(2005) Spectral Analysis of Signals. (1 edition.). Upper Saddle River, N.J: Prentice Hall
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Wise, D. K.(2006) The modified Chamberlin and Zölzer filter structures. In Proc. of the 9th Int. Conference on Digital Audio Effects (DAFx-06) (Vol. 2, p. 3).
Wish14
Wishnick, A. (2014) Time-Varying Filters for Musical Applications. In DAFx (pp. 69–76).