# Signal processing

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

March 19, 2015 — January 5, 2018

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?

## 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

- Tom O’Haver has a free online textbook with extensive OCTAVE/MATLAB code, A Pragmatic Introduction to Signal Processing. 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.

## 5 References

*Digital signal processing: signals, systems and filters*.

*Supplement to the Journal of the Royal Statistical Society*.

*Time Series Analysis: Forecasting and Control*. Wiley Series in Probability and Statistics.

*Musical applications of microprocessors*.

*International Journal of Approximate Reasoning*.

*An Introduction to Statistical Signal Processing*.

*Statistics Surveys*.

*Linear Estimation*. Prentice Hall Information and System Sciences Series.

*Fundamentals of Statistical Signal Processing*. Prentice Hall Signal Processing Series.

*Journal of the Audio Engineering Society*.

*Proceedings of the IEEE*.

*IEEE Journal of Selected Topics in Signal Processing*.

*Digital Spectral Analysis with Applications*.

*Proceedings of the Royal Society of London*.

*Isis*.

*Mathematical Methods and Algorithms for Signal Processing*.

*IEEE Transactions on Acoustics, Speech and Signal Processing*.

*IEEE Signal Processing Letters*.

*Transactions of the American Institute of Electrical Engineers*.

*Discrete-Time Signal Processing*.

*Signals, Systems and Inference*.

*Introduction to Signal Processing*. Prentice Hall Signal Processing Series.

*arXiv:1501.00320 [Cs, Math]*.

*Signal processing for communications*. Communication and information sciences.

*Signal Processing*.

*Transactions of the American Institute of Electrical Engineers, Part II: Applications and Industry*.

*The Astrophysical Journal Supplement Series*.

*Proceedings of the IRE*.

*Introduction to Digital Filters with Audio Applications*.

*Spectral Analysis of Signals*.

*Discrete Random Signals and Statistical Signal Processing*.

*DAFx*.