Hostname: page-component-cd9895bd7-lnqnp Total loading time: 0 Render date: 2024-12-29T05:14:20.714Z Has data issue: false hasContentIssue false
  • English
  • Français

Measurement of a wandering signal amid noise

Published online by Cambridge University Press:  14 July 2016

E. J. Hannan
E. J. Hannan*
Affiliation:
Australian National University
Get access Rights & Permissions [Opens in a new window]

Abstract

A formula is given for the response function of a filter which extracts a signal generated by a non-stationary process from amid noise. The non-stationarity is due to the presence of zeros on the unit circle of the function characterising the difference equation generating the signal. The signal is broken into a trend component and a stochastic integral in which t occurs only through the factor exp it λ and it is shown that the filter which optimally extracts the latter perfectly represents the former. The considerations cover the case of a vector series. Applications to problems in seasonal variation measurement are indicated.

Type
Research Papers
Information
Journal of Applied Probability , Volume 4 , Issue 1 , November 1967 , pp. 90 - 102
Copyright
Copyright © Applied Probability Trust 

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

References

[1] Hannan, E. J. (1964) The estimation of a changing seasonal pattern. J. Amer. Statist. Ass. 59, 1063–1077.CrossRefGoogle Scholar
[2] Hoffman, K. (1962) Banach Spaces of Analytic Functions. Prentice-Hall.Google Scholar
[3] Macduffee, C. C. (1956) The Theory of Matrices. Chelsea, New York.Google Scholar
[4] Potapov, V. P. (1955) The multiplicative structure of J-contractive matrix functions. Trudy Moskov. Mat. Obšc. 4, 125–236 (Amer. Math. Soc. Translation 15, 131–244).Google Scholar
[5] Sobel, E. (1965) Extraction of Slowly Changing Signals and of Sums of Accumulating Sequences. Thesis, The Johns Hopkins University, Baltimore.Google Scholar
[6] Sobel, E. (1966) Prediction of a noise corrupted, non-stationary signal (to appear).Google Scholar
[7] Whittle, P. (1963) Prediction and Regulation. English Universities Press, London.Google Scholar
[8] Wiener, N. and Masani, P. (1957) The prediction theory of multivariate stochastic processes. Acta Math. 98, 111–150.Google Scholar