Skip to main content
SpringerLink
Log in

Statistical Signal Processing

  • Reference work entry
  • First Online:
International Encyclopedia of Statistical Science

  • 166 Accesses

Signal processing may broadly be considered to involve the recovery of information from physical observations. The received signals is usually disturbed by thermal, electrical, atmospheric or intentional interferences. Due to the random nature of the signal, statistical techniques play an important role in signal processing. Statistics is used in the formulation of appropriate models to describe the behavior of the system, the development of appropriate techniques for estimation of model parameters, and the assessment of model performances. Statistical Signal Processing basically refers to the analysis of random signals using appropriate statistical techniques. The main purpose of this article is to introduce different signal processing models and different statistical and computational issues involved in solving them.

The Multiple Sinusoids Model

The multiple sinusoids model may be expressed as

$$y(t) ={ \sum \limits _{k=1}^{M}}\{{A}_{ k}\cos ({\omega }_{k}t) + {B}_{k}\sin {\omega...

This is a preview of subscription content, log in via an institution to check access.

Access this chapter

Log in via an institution
Chapter
USD 29.95
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD 1,100.00
Price excludes VAT (USA)
  • Available as EPUB and PDF
  • Read on any device
  • Instant download
  • Own it forever
Hardcover Book
USD 549.99
Price excludes VAT (USA)
  • Durable hardcover edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info

Tax calculation will be finalised at checkout

Purchases are for personal use only

Institutional subscriptions

References and Further Reading

  • Bose NK, Rao CR (1993) Signal processing and its applications. Handbook of Statistics, 10, North-Holland, Amsterdam

    Google Scholar 

  • Brillinger D (1987) Fitting cosines: some procedures and some physical examples. In MacNeill IB, Umphrey GJ (eds) Applied statistics, stochastic processes and sampling theory. Reidel, Dordrecht

    Google Scholar 

  • Fisher RA (1929) Tests of significance in Harmonic analysis. Proc R Soc London A 125:54–59

    MATH  Google Scholar 

  • Hannan EJ (1973) The estimation of frequencies. J Appl Probab 10:510–519

    MathSciNet  MATH  Google Scholar 

  • Kay SM (1987) Modern spectral estimation. Prentice Hall, New York, NY

    Google Scholar 

  • Kundu D (1997) Asymptotic theory of the least squares estimators of sinusoidal signal. Statistics 30:221–238

    MathSciNet  MATH  Google Scholar 

  • Pillai SU (1989) Array signal processing. Springer, New York, NY

    Google Scholar 

  • Prasad A (2009) Some non-linear regression models and their applications in statistical signal processing. PhD thesis, Indian Institute of Technology Kanpur, India

    Google Scholar 

  • Prasad A, Kundu D (2009) Modeling and estimation of symmetric color textures. Sankhya Ser B 71(1):30–54

    MathSciNet  MATH  Google Scholar 

  • Quinn BG, Hannan EJ (2001) The estimation and tracking of frequency. Cambridge University Press, Cambridge, UK

    MATH  Google Scholar 

  • Srinath MD, Rajasekaran PK, Viswanathan R (1996) Introduction to statistical processing with applications. Prentice-Hall, Englewood Cliffs, NJ

    Google Scholar 

  • Stoica P (1993) List of references on spectral estimation. Signal Process 31:329–340

    Google Scholar 

  • Zhang H, Mandrekar V (2001) Estimation of hidden frequencies for 2-D stationary processes. J Time Ser Anal 22:613–629

    MathSciNet  MATH  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Indian Institute of Technology Kanpur, Kanpur, India

    Debasis Kundu

Authors
  1. Debasis Kundu
    View author publications

    You can also search for this author in PubMed Google Scholar

Editor information

Editors and Affiliations

  1. Department of Statistics and Informatics, Faculty of Economics, University of Kragujevac, City of Kragujevac, Serbia

    Miodrag Lovric

Rights and permissions

Reprints and permissions

Copyright information

© 2011 Springer-Verlag Berlin Heidelberg

About this entry

Cite this entry

Kundu, D. (2011). Statistical Signal Processing. In: Lovric, M. (eds) International Encyclopedia of Statistical Science. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-04898-2_552

Download citation

Publish with us

Policies and ethics

Search

Navigation