The Living Thing / Notebooks :

Signal processing

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

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

Contents

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?

Sine + Noise + Transients

Resources

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

Refs

Anto05
Antoniou, A. (2005) Digital signal processing: signals, systems and filters. . New York: McGraw-Hill
Bart46
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. DOI.
BJRL16
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. Statistics Surveys, 4, 232–274. DOI.
KaSH00
Kailath, T., Sayed, A. H., & Hassibi, B. (2000) Linear estimation. . Upper Saddle River, N.J: Prentice Hall
Kay93
Kay, S. M.(1993) Fundamentals of statistical signal processing. . Englewood Cliffs, N.J: Prentice-Hall PTR
Laro07
Laroche, J. (2007) On the Stability of Time-Varying Recursive Filters. Journal of the Audio Engineering Society, 55(6), 460–471.
Marp87
Marple, S. L., Jr. (1987) Digital spectral analysis with applications.
MoSt00
Moon, T. K., & Stirling, W. C.(2000) Mathematical methods and algorithms for signal processing. . Upper Saddle River, NJ: Prentice Hall
Moor74
Moorer, J. . (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.
NaIV02
Narasimha, M. J., Ignjatovic, A., & Vaidyanathan, P. P.(2002) Chromatic derivative filter banks. IEEE Signal Processing Letters, 9(7), 215–216. DOI.
Nyqu28
Nyquist, H. (1928) Certain Topics in Telegraph Transmission Theory. Transactions of the American Institute of Electrical Engineers, 47(2), 617–644. DOI.
OpSB99
Oppenheim, A. V., Schafer, R. W., & Buck, J. R.(1999) Discrete-time signal processing. (2nd ed.). Upper Saddle River, N.J: Prentice Hall
Orfa96
Orfanidis, S. J.(1996) Introduction to signal processing. . Englewood Cliffs, N.J: Prentice Hall
PaRa15
Pawar, S., & Ramchandran, K. (2015) A robust sub-linear time R-FFAST algorithm for computing a sparse DFT. ArXiv:1501.00320 [Cs, Math].
PrVe08
Prandoni, P., & Vetterli, M. (2008) Signal processing for communications. . Lausanne: EPFL Press
PrLu13
Proietti, T., & Luati, A. (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
QiCh94
Qian, S., & Chen, D. (1994) Signal representation using adaptive normalized Gaussian functions. Signal Processing, 36(1), 1–11. DOI.
RaZa52
Ragazzini, J. R., & Zadeh, L. A.(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.
Scar81
Scargle, J. D.(1981) Studies in astronomical time series analysis I-Modeling random processes in the time domain. The Astrophysical Journal Supplement Series, 45, 1–71.
Shan49
Shannon, C. E.(1949) Communication in the Presence of Noise. Proceedings of the IRE, 37(1), 10–21. DOI.
Smit07
Smith, J. O.(2007) Introduction to Digital Filters with Audio Applications. . http://www.w3k.org/books/: W3K Publishing
StMo05
Stoica, P., & Moses, R. L.(2005) Spectral Analysis of Signals. (1 edition.). Upper Saddle River, N.J: Prentice Hall
Ther92
Therrien, C. W.(1992) Discrete random signals and statistical signal processing. . Englewood Cliffs, NJ: Prentice Hall
Wish14
Wishnick, A. (2014) Time-Varying Filters for Musical Applications. In DAFx (pp. 69–76).