Evolving Systems

, Volume 10, Issue 2, pp 285–294 | Cite as

An evolutionary spectral representation for blind separation of biosignals

  • Seda SenayEmail author
Original Paper


Blind source separation (BSS) methods are used to separate sources from a mixed observations with very little prior knowledge of the mixing coefficients or sources. In this paper we propose an evolutionary spectral representation to implement BSS. Introduced by Priestley, evolutionary spectral theory generalizes the definition of spectrum for nonstationary processes. Under certain conditions, the evolutionary spectrum at each instant of time can be estimated from a single realization of a process such that it is possible to study processes with changing spectral patterns. In particular we are interested in the problem of separation of individual biosignals from electrophysiological recordings mixed by volume conduction. As biosignals such as electrocardiogram and electroencephalogram recordings are prime examples of nonstationary signals, evolutionary spectral representations can be used for the analysis of them. Our proposed evolutionary spectral representation is based on the discrete prolate spheroidal sequences (DPSS). Also known as Slepian sequences, the DPSS are defined to be the sequences with maximum spectral concentration for a given duration and bandwidth. Using the relation between discrete evolutionary transform and evolutionary periodogram, we derive the Slepian evolutionary spectrum. After the evolutionary spectrum is computed, we implement it for the BSS problem and compare with the well known time-frequency methods (Wigner-Ville distribution and S-transform) for performance evaluation.


  1. Belouchrani A, Amin A (1998) Blind source separation based on time-frequency signal representation. IEEE Trans Signal Process 46:2888–2897CrossRefGoogle Scholar
  2. Belouchrani A, Meraim K, Cardoso JF, Moulines E (1997) A blind source separation techniques using second-order statistics. IEEE Trans Signal Process 45:434–444CrossRefGoogle Scholar
  3. Boashash B (1991) Advances in spectrum analysis and array processing. Time-frequency signal analysis, vol 1. Prentice-Hall, Englewood CliffsGoogle Scholar
  4. Boashash B (2003) Time-frequency signal analysis and processing: a comprehensive reference. Elsevier, OxfordGoogle Scholar
  5. Bohme JF (1979) Array processing in semi-homogeneous random fields. In: Proc. Septieme Colloque Sur le Traitment di Signal est Ses Applications, pp. 104/1–104/4Google Scholar
  6. Cardoso JF, Souloumiac A (1993) Blind beamforming for non Gaussian signals. Proc Inst Elect Eng 140:362–370Google Scholar
  7. Cichocki A, Amari S, Siwek K, et al (2007) ICALAB toolboxes. Scholar
  8. Cohen L (1995) Time-frequency analysis. Prentice-Hall, Englewood CliffsGoogle Scholar
  9. Coivunen V, Enescu M, Oja E (2001) Adaptive algorithm for blind separation from noisy time varying mixture. Neural Comput 13:2339–2357CrossRefzbMATHGoogle Scholar
  10. Delorme A, Palme J, Onton J (2012) Independent EEG sources are dipolar. Plos one 7:e30135CrossRefGoogle Scholar
  11. Delorme A, Sejnowski T, Makeig S (2007) Enhanced detection of artifacts in EEG data using higher order statistics and independent analysis. J Neuroimage 34:1443–1449CrossRefGoogle Scholar
  12. Everson, R, Roberts S (2018) Particle filters for Non-Stationary ICA. Adv Independent Component Anal 23–41Google Scholar
  13. Fevotte C, Doncarli C (2004) Two contributions to blind source separation using time-frequency distributions. IEEE Signal Process Lett 11:386–389CrossRefGoogle Scholar
  14. Fujita K (2012) Remarks on a method to estimate the number of sources in blind source separation. In: International conference on wavelet analysis and pattern recognition (ICWAPR), pp. 378–383, 2012, ISSN 2158-5695Google Scholar
  15. Johnson DH, Dudgeon DE (1993) Array signal processing: concepts and techniques. Prentice-Hall, Englewood CliffszbMATHGoogle Scholar
  16. Kayhan AS, El-Jaroudi A, Chaparro LF (1994) Evolutionary periodogram for nonstationary signals. IEEE Trans Signal Process 42:1527–1536CrossRefGoogle Scholar
  17. Kayhan AS, Moeness GA (2000) Spatial evolutionary spectrum for DOA estimation and blind signal estimation. IEEE Trans Signal Process 48:791–797CrossRefGoogle Scholar
  18. Kayhan AS, El-Jaroudi A, Chaparro LF (1992) Wold-cramer evolutionary spectral estimators. In: Proc. IEEE-SP Int. Sympos. time-frequency time-scale analysis, Victoria, Canada, pp. 115–118Google Scholar
  19. Liebeherr J, Markus F, Shahrokh V (2016) A system-theoretic approach to bandwidth estimation. IEEE/ACM Trans Netw 18(4):1040–1053CrossRefGoogle Scholar
  20. Liebeherr J, Markus F, Shahrokh V (2007) A min-plus system interpretation of bandwidth estimation. In: INFOCOM 26th IEEE international conference on computer communicationsGoogle Scholar
  21. Makeig S, Bell AJ, Jun TP et al (1996) Independent component analysis of EEG data. J Adv Neural Inform Process Syst 145–151Google Scholar
  22. Marques M., et al (2006) The Papoulis-Gerchberg algorithm with unknown signal bandwidth. In: International conference image analysis and recognition. Springer, Berlin, HeidelbergGoogle Scholar
  23. Melard G, Schutter AH (1989) Contributions to evolutionary spectral theory. J Time Ser Anal 10:41–63MathSciNetCrossRefzbMATHGoogle Scholar
  24. Moghtaderi A, Takahara G, Thomson DJ (2009) Evolutionary spectrum estimation for uniformly modulated processes with improved frequency resolution. In: IEEE Workshop on statistical signal processingGoogle Scholar
  25. Moore IC, Cada M (2004) Prolate spheroidal wave functions: An introduction to the Slepian series and its properties. Appl Comput Harmonic Anal 16:208–230MathSciNetCrossRefzbMATHGoogle Scholar
  26. Oh J, Senay S, Chaparro LF (2010) Signal reconstruction from nonuniformly spaced samples using evolutionary Slepian transform-based POCS. EURASIP J Adv Signal Process (special issue on applications of time-frequency signal processing in wireless communications and bioengineering)Google Scholar
  27. Pal M, Roy R, Basu J, Bepari M (2013) Blind source separation: a review and analysis. In: Asian spoken language research and evaluation conference, pp. 1–5Google Scholar
  28. Priestley MB (1981) Spectral analysis and time series. Academic Press, CambridgezbMATHGoogle Scholar
  29. Priestly MB (1967) Power spectral analysis of nonstationary random processes. J Sound Vib 6:86–97CrossRefGoogle Scholar
  30. Sekihara K, Nagarajan S, Poeppel D, Miyashita Y (1999) Time-frequency MEG-MUSIC algorithm. IEEE Trans Med Imag 18:92–97CrossRefGoogle Scholar
  31. Simons FJ, Loris I, Brevdo E, Daubechies IC (2018) Wavelets and wavelet-like transforms on the sphere and their application to geophysical data inversion.
  32. Slepian D (1962) Prolate spheroidal wave functions, Fourier analysis and uncertainty IV: extensions to many dimensions; generalized prolate spheroidal functions. Bell Syst Techn J 43:3009–3057CrossRefzbMATHGoogle Scholar
  33. Stankovic LJ (1994) A method for time-frequency analysis. IEEE Trans Signal Proc 42:225–229CrossRefGoogle Scholar
  34. Suleesathira R, Chaparro LF, Akan A (1998) Discrete evolutionary transform for time-frequency analysis. In: Proc. Asilomar conference on Sig., Sys. and Comp., pp. 812–816Google Scholar
  35. Tong L, Liu R, Soon V, Huang Y (1991) Indeterminacy and identifiability of blind identification. IEEE Trans Circuits Syst 38:499–509CrossRefzbMATHGoogle Scholar
  36. Tsiakoulis P, Alexandros P, Dimitrios D (2013) Instantaneous frequency and bandwidth estimation using filterbank arrays. In: Acoustics Speech Signal Process 2013 IEEE international conferenceGoogle Scholar
  37. Walter GG, Shen X (2003) Sampling with prolate spheroidal functions. Am Math Soc 41–227Google Scholar
  38. Wang X, Yong G (2016) Stochastic resonance for estimation of a signals bandwidth under low SNR. Analog Integr Circuits Signal Process 89(1):263–269CrossRefGoogle Scholar
  39. Yuan Y, Tan B, Zhou G, Zhang J (2008) Source number estimation and separation algorithms of underdetermined blind separation. China Ser F-Inf Sci 51:1623. CrossRefzbMATHGoogle Scholar

Copyright information

© Springer-Verlag GmbH Germany, part of Springer Nature 2018

Authors and Affiliations

  1. 1.New Mexico Institute of Mining and TechnologySocorroUSA

Personalised recommendations