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 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.

## 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?

## Sampling

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

## 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 smart at unexpected and enlightening perspectives.

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

- PaRa15: Sameer Pawar, Kannan Ramchandran (2015) A robust sub-linear time R-FFAST algorithm for computing a sparse DFT.
*ArXiv:1501.00320 [Cs, Math]*. - GrDa10: Robert M. Gray, Lee D. Davisson (2010)
*An introduction to statistical signal processing*. Cambridge: Cambridge University Press - Nyqu28: H. Nyquist (1928) Certain Topics in Telegraph Transmission Theory.
*Transactions of the American Institute of Electrical Engineers*, 47(2), 617–644. DOI - NaIV02: M. J. Narasimha, A. Ignjatovic, P. P. Vaidyanathan (2002) Chromatic derivative filter banks.
*IEEE Signal Processing Letters*, 9(7), 215–216. DOI - Shan49: C. E. Shannon (1949) Communication in the Presence of Noise.
*Proceedings of the IRE*, 37(1), 10–21. DOI - Anto05: Andreas Antoniou (2005)
*Digital signal processing: signals, systems and filters*. New York: McGraw-Hill - Marp87: S. Lawrence Marple Jr. (1987)
*Digital spectral analysis with applications* - Ther92: Charles W. Therrien (1992)
*Discrete random signals and statistical signal processing*. Englewood Cliffs, NJ: Prentice Hall - OpSB99: Alan V. Oppenheim, Ronald W. Schafer, John R. Buck (1999)
*Discrete-time signal processing*. Upper Saddle River, N.J: Prentice Hall - Kay93: Steven M. Kay (1993)
*Fundamentals of statistical signal processing*. Englewood Cliffs, N.J: Prentice-Hall PTR - Smit07: Julius O. Smith (2007)
*Introduction to Digital Filters with Audio Applications*. http://www.w3k.org/books/: W3K Publishing - Orfa96: Sophocles J. Orfanidis (1996)
*Introduction to signal processing*. Englewood Cliffs, N.J: Prentice Hall - KaSH00: Thomas Kailath, Ali H. Sayed, Babak Hassibi (2000)
*Linear estimation*. Upper Saddle River, N.J: Prentice Hall - MoSt00: Todd K. Moon, Wynn C. Stirling (2000)
*Mathematical methods and algorithms for signal processing*. Upper Saddle River, NJ: Prentice Hall - Cham85: Hal Chamberlin (1985)
*Musical applications of microprocessors*. Hasbrouck Heights, N.J: Hayden Book Co. - Laro07: Jean Laroche (2007) On the Stability of Time-Varying Recursive Filters.
*Journal of the Audio Engineering Society*, 55(6), 460–471. - Bart46: M. S. Bartlett (1946) On the Theoretical Specification and Sampling Properties of Autocorrelated Time-Series.
*Supplement to the Journal of the Royal Statistical Society*, 8(1), 27–41. DOI - PrVe08: Paolo Prandoni, Martin Vetterli (2008)
*Signal processing for communications*. Lausanne: EPFL Press - QiCh94: Shie Qian, Dapang Chen (1994) Signal representation using adaptive normalized Gaussian functions.
*Signal Processing*, 36(1), 1–11. DOI - StMo05: Petre Stoica, Randolph L. Moses (2005)
*Spectral Analysis of Signals*. Upper Saddle River, N.J: Prentice Hall - Scar81: Jeffrey D Scargle (1981) Studies in astronomical time series analysis I-Modeling random processes in the time domain.
*The Astrophysical Journal Supplement Series*, 45, 1–71. - RaZa52: J. R. Ragazzini, L. A. Zadeh (1952) The analysis of sampled-data systems.
*Transactions of the American Institute of Electrical Engineers, Part II: Applications and Industry*, 71(5), 225–234. DOI - HoLD10: Scott H. Holan, Robert Lund, Ginger Davis (2010) The ARMA alphabet soup: A tour of ARMA model variants.
*Statistics Surveys*, 4, 232–274. DOI - PrLu13: Tommaso Proietti, Alessandra Luati (2013) The Exponential Model for the Spectrum of a Time Series: Extensions and Applications (SSRN Scholarly Paper No. ID 2254038). Rochester, NY: Social Science Research Network
- Moor74: J.A Moorer (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 - BJRL16: George E. P. Box, Gwilym M. Jenkins, Gregory C. Reinsel, Greta M. Ljung (2016)
*Time series analysis: forecasting and control*. Hoboken, New Jersey: John Wiley & Sons, Inc - Wish14: Aaron Wishnick (2014) Time-Varying Filters for Musical Applications. In DAFx (pp. 69–76).