Signal processing

That which you study for 4 years in order to design trippy music visualisers

March 19, 2015 — January 5, 2018

dynamical systems
Hilbert space
signal processing
statistics
time series

Signal processing is a discipline dedicated to the engineering end of stochastic process inference and prediction, especially linear time series.

There are various translation difficulties for statisticians; “Testing” = “Detection”, “Linear Filter” = “ARIMA model”, estimation of parameters is system identification, estimation of hidden states is filtering, and so on.

This is a general note to mention that the field exists. Most useful information is under sub-fields, e.g. machine listening, for some signal processing tricks for audio, or feedback systems, for some models particularly appropriate to systems that accept their own output as input, etc.

See also orthogonal basis decompositions. There are close connections to optimal control.

Anyway, I don’t need to explain that here; there are so many software engineers involved with it. The internet is full of interactive diagrammy textbooks to fill that niche.

But here are some notes on some nuggets of interest that I wasn’t sure where else to file.

1 Signal processing on graphs

Nothing to say here yet, but I feel I should raid the literature of the EPFL Signal processing lab 2 who make a specialty of it.

2 Stochastic decomposition

Model for decomposing harmonic sound into pure tones plus other stuff (aside: why not other periodic functions?) This is just some kind of parametric state or system inference, right?

Sine + Noise + Transients

3 Sampling

Signal sampling is the art of turning continuous signals into discrete ones and back again.

4 Resources

See also the slightly more specialised and overlapping list of filter design resources.

5 References

Antoniou. 2005. Digital signal processing: signals, systems and filters.
Bartlett. 1946. “On the Theoretical Specification and Sampling Properties of Autocorrelated Time-Series.” Supplement to the Journal of the Royal Statistical Society.
Box, Jenkins, Reinsel, et al. 2016. Time Series Analysis: Forecasting and Control. Wiley Series in Probability and Statistics.
Burred, Ponsot, Goupil, et al. 2018. “CLEESE: An Open-Source Audio-Transformation Toolbox for Data-Driven Experiments in Speech and Music Cognition.” Preprint.
Chamberlin. 1985. Musical applications of microprocessors.
Cox, van de Laar, and de Vries. 2019. “A Factor Graph Approach to Automated Design of Bayesian Signal Processing Algorithms.” International Journal of Approximate Reasoning.
Gray, and Davisson. 2010. An Introduction to Statistical Signal Processing.
Holan, Lund, and Davis. 2010. “The ARMA Alphabet Soup: A Tour of ARMA Model Variants.” Statistics Surveys.
Kailath, Sayed, and Hassibi. 2000. Linear Estimation. Prentice Hall Information and System Sciences Series.
Kay. 1993. Fundamentals of Statistical Signal Processing. Prentice Hall Signal Processing Series.
Laroche. 2007. “On the Stability of Time-Varying Recursive Filters.” Journal of the Audio Engineering Society.
Loeliger, Dauwels, Hu, et al. 2007. “The Factor Graph Approach to Model-Based Signal Processing.” Proceedings of the IEEE.
Manton. 2013. “A Primer on Stochastic Differential Geometry for Signal Processing.” IEEE Journal of Selected Topics in Signal Processing.
Marple. 1987. Digital Spectral Analysis with Applications.
Maxwell. 1867. “On Governors.” Proceedings of the Royal Society of London.
Mayr. 1971. “Maxwell and the Origins of Cybernetics.” Isis.
Moon, and Stirling. 2000. Mathematical Methods and Algorithms for Signal Processing.
Moorer. 1974. “The Optimum Comb Method of Pitch Period Analysis of Continuous Digitized Speech.” IEEE Transactions on Acoustics, Speech and Signal Processing.
Narasimha, Ignjatovic, and Vaidyanathan. 2002. “Chromatic Derivative Filter Banks.” IEEE Signal Processing Letters.
Nyquist. 1928. “Certain Topics in Telegraph Transmission Theory.” Transactions of the American Institute of Electrical Engineers.
Oppenheim, Schafer, and Buck. 1999. Discrete-Time Signal Processing.
Oppenheim, and Verghese. 2015. Signals, Systems and Inference.
Orfanidis. 1996. Introduction to Signal Processing. Prentice Hall Signal Processing Series.
Pawar, and Ramchandran. 2015. “A Robust Sub-Linear Time R-FFAST Algorithm for Computing a Sparse DFT.” arXiv:1501.00320 [Cs, Math].
Prandoni, and Vetterli. 2008. Signal processing for communications. Communication and information sciences.
Proietti, and Luati. 2013. “The Exponential Model for the Spectrum of a Time Series: Extensions and Applications.” SSRN Scholarly Paper ID 2254038.
Qian, and Chen. 1994. “Signal Representation Using Adaptive Normalized Gaussian Functions.” Signal Processing.
Ragazzini, and Zadeh. 1952. “The Analysis of Sampled-Data Systems.” Transactions of the American Institute of Electrical Engineers, Part II: Applications and Industry.
Scargle. 1981. “Studies in Astronomical Time Series Analysis. I-Modeling Random Processes in the Time Domain.” The Astrophysical Journal Supplement Series.
Shannon. 1949. “Communication in the Presence of Noise.” Proceedings of the IRE.
Smith. 2007. Introduction to Digital Filters with Audio Applications.
Stoica, and Moses. 2005. Spectral Analysis of Signals.
Therrien. 1992. Discrete Random Signals and Statistical Signal Processing.
Wishnick. 2014. “Time-Varying Filters for Musical Applications.” In DAFx.