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 very 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 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.

## 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.

## 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?

## Resources

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

- Tom O’Haver has a free online textbook with extensive OCTAVE/MATLAB code, A Pragmatic Introduction to Signal Processing. Very skewed towards pure Fourier domain techniques.
- Textbook: Paolo Prandoni and Martin Vetterli, Signal Processing for Communications is available online. Vetterli is very smart at unexpected and enlightening perspectives; I’m a fan.
- Textbook: Antoniou has been generally recommended if you want to get hands-on ASAP. (Anto05)
- Textbook: Orfandis’ opus is free online. (Orfa96)
- Course notes/textbook: Oppenheim and Verghese, Signals, Systems, and Inference is free online.
- Numerical tours of signal processing gives python, julia and matlab tours of signal processing. Better consumed through their github repo.

## Refs

- Anto05
- Antoniou, A. (2005) Digital signal processing: signals, systems and filters. . New York: McGraw-Hill
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- Bartlett, M. S.(1946) On the Theoretical Specification and Sampling Properties of Autocorrelated Time-Series.
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- Box, G. E. P., Jenkins, G. M., Reinsel, G. C., & Ljung, G. M.(2016) Time series analysis: forecasting and control. (Fifth edition.). Hoboken, New Jersey: John Wiley & Sons, Inc
- Cham85
- Chamberlin, H. (1985) Musical applications of microprocessors. (2nd ed.). Hasbrouck Heights, N.J: Hayden Book Co.
- GrDa10
- Gray, R. M., & Davisson, L. D.(2010) An introduction to statistical signal processing. . Cambridge: Cambridge University Press
- HoLD10
- Holan, S. H., Lund, R., & Davis, G. (2010) The ARMA alphabet soup: A tour of ARMA model variants.
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*ArXiv:1501.00320 [Cs, Math]*. - PrVe08
- Prandoni, P., & Vetterli, M. (2008) Signal processing for communications. . Lausanne: EPFL Press
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- Smith, J. O.(2007) Introduction to Digital Filters with Audio Applications. . http://www.w3k.org/books/: W3K Publishing
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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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