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.
Signal sampling is the art of turning continuous signals into discrete ones and back again.
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. (Antoniou 2005)
- Textbook: Orfandis’ opus is free online. (Antoniou 2005)
- 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.
Antoniou, Andreas. 2005. Digital Signal Processing: Signals, Systems and Filters. New York: McGraw-Hill.
Bartlett, M. S. 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. https://doi.org/10.2307/2983611.
Box, George E. P., Gwilym M. Jenkins, Gregory C. Reinsel, and Greta M. Ljung. 2016. Time Series Analysis: Forecasting and Control. Fifth edition. Wiley Series in Probability and Statistics. Hoboken, New Jersey: John Wiley & Sons, Inc.
Burred, Juan José, Emmanuel Ponsot, Louise Goupil, Marco Liuni, and Jean-Julien Aucouturier. 2018. “CLEESE: An Open-Source Audio-Transformation Toolbox for Data-Driven Experiments in Speech and Music Cognition.” Preprint. Neuroscience. https://doi.org/10.1101/436477.
Chamberlin, Hal. 1985. Musical Applications of Microprocessors. 2nd ed. Hasbrouck Heights, N.J: Hayden Book Co.
Cox, Marco, Thijs van de Laar, and Bert de Vries. 2019. “A Factor Graph Approach to Automated Design of Bayesian Signal Processing Algorithms.” International Journal of Approximate Reasoning 104 (January): 185–204. https://doi.org/10.1016/j.ijar.2018.11.002.
Gray, Robert M., and Lee D. Davisson. 2010. An Introduction to Statistical Signal Processing. Cambridge: Cambridge University Press. https://ee.stanford.edu/~gray/sp.html.
Holan, Scott H., Robert Lund, and Ginger Davis. 2010. “The ARMA Alphabet Soup: A Tour of ARMA Model Variants.” Statistics Surveys 4: 232–74. https://doi.org/10.1214/09-SS060.
Kailath, Thomas, Ali H. Sayed, and Babak Hassibi. 2000. Linear Estimation. Prentice Hall Information and System Sciences Series. Upper Saddle River, N.J: Prentice Hall.
Kay, Steven M. 1993. Fundamentals of Statistical Signal Processing. Prentice Hall Signal Processing Series. Englewood Cliffs, N.J: Prentice-Hall PTR.
Laroche, Jean. 2007. “On the Stability of Time-Varying Recursive Filters.” Journal of the Audio Engineering Society 55 (6): 460–71. http://www.aes.org/e-lib/browse.cfm?elib=14168.
Loeliger, Hans-Andrea, Justin Dauwels, Junli Hu, Sascha Korl, Li Ping, and Frank R. Kschischang. 2007. “The Factor Graph Approach to Model-Based Signal Processing.” Proceedings of the IEEE 95 (6): 1295–1322. https://doi.org/10.1109/JPROC.2007.896497.
Manton, Jonathan H. 2013. “A Primer on Stochastic Differential Geometry for Signal Processing.” IEEE Journal of Selected Topics in Signal Processing 7 (4): 681–99. https://doi.org/10.1109/JSTSP.2013.2264798.
Marple, S. Lawrence, Jr. 1987. Digital Spectral Analysis with Applications. http://adsabs.harvard.edu/abs/1987ph...book.....M.
Moon, Todd K., and Wynn C. Stirling. 2000. Mathematical Methods and Algorithms for Signal Processing. Upper Saddle River, NJ: Prentice Hall.
Moorer, J. A. 1974. “The Optimum Comb Method of Pitch Period Analysis of Continuous Digitized Speech.” IEEE Transactions on Acoustics, Speech and Signal Processing 22 (5): 330–38. https://doi.org/10.1109/TASSP.1974.1162596.
Narasimha, M. J., A. Ignjatovic, and P. P. Vaidyanathan. 2002. “Chromatic Derivative Filter Banks.” IEEE Signal Processing Letters 9 (7): 215–16. https://doi.org/10.1109/LSP.2002.801720.
Nyquist, H. 1928. “Certain Topics in Telegraph Transmission Theory.” Transactions of the American Institute of Electrical Engineers 47 (2): 617–44. https://doi.org/10.1109/T-AIEE.1928.5055024.
Oppenheim, Alan V., Ronald W. Schafer, and John R. Buck. 1999. Discrete-Time Signal Processing. 2nd ed. Upper Saddle River, N.J: Prentice Hall.
Oppenheim, Alan V., and George C. Verghese. 2015. Signals, Systems and Inference. Prentice Hall.
Orfanidis, Sophocles J. 1996. Introduction to Signal Processing. Prentice Hall Signal Processing Series. Englewood Cliffs, N.J: Prentice Hall. http://www.ece.rutgers.edu/~orfanidi/intro2sp/orfanidis-i2sp.pdf.
Pawar, Sameer, and Kannan Ramchandran. 2015. “A Robust Sub-Linear Time R-FFAST Algorithm for Computing a Sparse DFT,” January. http://arxiv.org/abs/1501.00320.
Prandoni, Paolo, and Martin Vetterli. 2008. Signal Processing for Communications. Communication and Information Sciences. Lausanne: EPFL Press.
Proietti, Tommaso, and Alessandra Luati. 2013. “The Exponential Model for the Spectrum of a Time Series: Extensions and Applications.” SSRN Scholarly Paper ID 2254038. Rochester, NY: Social Science Research Network. http://papers.ssrn.com/abstract=2254038.
Qian, Shie, and Dapang Chen. 1994. “Signal Representation Using Adaptive Normalized Gaussian Functions.” Signal Processing 36 (1): 1–11. https://doi.org/10.1016/0165-1684(94)90174-0.
Ragazzini, J. R., and 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): 225–34. https://doi.org/10.1109/TAI.1952.6371274.
Scargle, Jeffrey D. 1981. “Studies in Astronomical Time Series Analysis. I-Modeling Random Processes in the Time Domain.” The Astrophysical Journal Supplement Series 45: 1–71.
Shannon, C. E. 1949. “Communication in the Presence of Noise.” Proceedings of the IRE 37 (1): 10–21. https://doi.org/10.1109/JRPROC.1949.232969.
Smith, Julius O. 2007. Introduction to Digital Filters with Audio Applications. http://www.w3k.org/books/: W3K Publishing. https://ccrma.stanford.edu/~jos/filters/filters.html.
Stoica, Petre, and Randolph L. Moses. 2005. Spectral Analysis of Signals. 1 edition. Upper Saddle River, N.J: Prentice Hall. http://user.it.uu.se/~ps/SAS-new.pdf.
Therrien, Charles W. 1992. Discrete Random Signals and Statistical Signal Processing. Englewood Cliffs, NJ: Prentice Hall.
Wishnick, Aaron. 2014. “Time-Varying Filters for Musical Applications.” In DAFx, 69–76. http://www.dafx14.fau.de/papers/dafx14_aaron_wishnick_time_varying_filters_for_.pdf.