Abstract
Mathematical definitions that are necessary to better understand blind signal processing are presented in this chapter. Due to limitation of the book’s length, we will present theoretical results only, omitting the process of proof. Interested readers who want to know more about the process of proof can refer to Refs. [1–7]
This is a preview of subscription content, log in via an institution to check access.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Preview
Unable to display preview. Download preview PDF.
References
Sorenson H (1980) Parameter estimation: Principles and problems. Marcel Dekker, New York
Mendel J (1995) Lessons in estimation theory for signal processing, communications, and control. Prentice Hall, New Jersey
Hyvarinen A, Karhunen J, Oja E (2001) Independent component analysis. Wiley, New York
Cichocki A, Amari S I (2002) Adaptive blind signal and image processing— Learning algorithms and applications. Wiley, New York
Shi X Z (2003) Signal processing and soft-computing. Higher Education Press, Beijing(Chinese)
Zhang H Y (2001) Theoretical and experimental studies of blind source separation. Dissertation, Shanghai Jiao Tong University (Chinese)
Shen X Z (2005) Study of algorithms of second and higher order blind signal processing. Dissertation, Shanghai Jiao Tong University (Chinese)
Adali T, Taehwan K, Calhoun V (2004) Independent component analysis by complex nonlinearities. In: ICASSP’ 04. Montreal, Quebec, 2004, 5(17–21): 525–528
Sawada H, Mukai R, Araki S et al (2003) A polar-coordinate based nonlinear function for frequency domain blind source separation. IEICE Transactions Fundamentals E86-A(3): 590–596
Smaragdis P (1998) Blind separation of convolved mixturess in the frequency domain. Neurocomputing 22(1): 21–34
Annemüller J, Sejnowski T J, Makeig S (2003) Complex spectral domain independent component analysis of electroencephalographic data. In: Proceedings of ICA-2003, Nara, 2003
Bingham E, Hyvärinen A (2000) A fast fixed-point algorithm for independent component analysis of complex-valued signals. Int. J. Neural Systems 10(1): 1–8
Sawada H, Mukai R, Araki S et al (2002) A polar-coordinate based activation function for frequency domain blind source separation. In: Proceeding of ICASSP, Orlando, 2002: I-1001–I-1004
Neeser F D, Massey J L (1993) Proper complex random processes with applications to information theory. IEEE Transactions on Information Theory 39(4): 1293–1302
Eriksson J, Koivunen V (2004) Complex-valued ICA using second order statistics. In: Proceedings of the 2004 IEEE Signal Processing Society Workshop on Machine Learning for Signal Processing, Brazil, 2004, pp 183–191
Author information
Authors and Affiliations
Rights and permissions
Copyright information
© 2011 Shanghai Jiao Tong University Press, Shanghai and Springer-Verlag Berlin Heidelberg
About this chapter
Cite this chapter
Shi, X. (2011). Mathematical Description of Blind Signal Processing. In: Blind Signal Processing. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-11347-5_2
Download citation
DOI: https://doi.org/10.1007/978-3-642-11347-5_2
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-642-11346-8
Online ISBN: 978-3-642-11347-5
eBook Packages: EngineeringEngineering (R0)