Measurement of a wandering signal amid noise

1967 ◽  
Vol 4 (1) ◽  
pp. 90-102 ◽  
Author(s):  
E. J. Hannan
Keyword(s):  
Seasonal Variation ◽  
Difference Equation ◽  
Unit Circle ◽  
Response Function ◽  
Stationary Process ◽  
Stochastic Integral ◽  
Trend Component ◽  
The Difference

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.

Measurement of a wandering signal amid noise

1967 ◽  
Vol 4 (01) ◽  
pp. 90-102 ◽  
Author(s):  
E. J. Hannan
Keyword(s):  
Seasonal Variation ◽  
Difference Equation ◽  
Unit Circle ◽  
Response Function ◽  
Stationary Process ◽  
Stochastic Integral ◽  
Trend Component ◽  
The Difference

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.

scholarly journals On Boundedness of Solutions of the Difference Equation xn+1=(pxn+qxn−1)/(1+xn) for q>1+p>1

2009 ◽  
Vol 2009 ◽  
pp. 1-11 ◽  
Author(s):  
Hongjian Xi ◽  
Taixiang Sun ◽  
Weiyong Yu ◽  
Jinfeng Zhao
Keyword(s):  
Difference Equation ◽  
Boundedness Of Solutions ◽  
The Difference

THE STUDY OF LONGITUDINAL AND LATITUDINAL VARIATION OF EQUATORIAL ELECTROJET SIGNATURE AT STATIONS WITHIN THE 96°MM AND 210°MM AFRICAN AND ASIAN SECTORS RESPECTIVELY UNDER QUIET CONDITIONS.

2021 ◽  
Vol 5 (2) ◽  
pp. 511-532
Author(s):  
Aniefiok Akpaneno ◽  
Matthew Joshua ◽  
K. R. Ekundayo
Keyword(s):  
Seasonal Variation ◽  
Geomagnetic Field ◽  
Satellite Communication ◽  
Equatorial Electrojet ◽  
Latitudinal Variation ◽  
Magnetic Data ◽  
Horizontal Magnetic Field ◽  
Baseline Values ◽  
The Difference ◽  
Current Systems

Solar quiet current (S_q) and Equatorial Electrojet (EEJ) are two current systems which are produced by electric current in the ionosphere.  The enhancement of the horizontal magnetic field is the EEJ. This research is needed for monitoring equatorial geomagnetic current which causes atmospheric instabilities and affects high frequency and satellite communication. This study presents the longitudinal and latitudinal variation of equatorial electrojet signature at stations within the 96°mm and 210°mm African and Asian sectors respectively during quiet condition. Data from eleven observatories were used for this study. The objectives was  to determine the longitudinal and latitudinal geomagnetic field variations during solar quiet conditions, Investigate monthly variation and diurnal transient seasonal variation; Measure the strength of the EEJ at stations within the same longitudinal sectors and find out the factors responsible for the longitudinal and latitudinal variation of EEJ. Horizontal (H) component of geomagnetic field for the year 2008 from Magnetic Data Acquisition System (MAGDAS) network were used for the study. The International Quiet Days (IQDs) were used to identify quiet days. Daily baseline values for each of the geomagnetic element H  were obtained.  The monthly average of the diurnal variation was found. The seasonal variation of dH was found. Results showed that: The longitudinal and latitudinal variation in the dH differs in magnitude from one station to another within the same longitude due to the difference in the influence of the EEJ on them.

scholarly journals An inequality with application to a difference equation

2004 ◽  
Vol 69 (3) ◽  
pp. 519-528 ◽  
Author(s):  
Jong-Yi Chen ◽  
Yunshyong Chow
Keyword(s):  
Heat Conduction ◽  
Difference Equation ◽  
Heat Conduction Problem ◽  
The Difference

In this paper we shall prove that for any 0 < d ≤ 2, holds for n ≥ 1.As an application, we shall then show that the following recursively defined sequence satisfies The difference equation above originates from a heat conduction problem studied by Myshkis (J. Difference Equ. Appl. 3(1997), 89–91).

On the difference equation

2012 ◽  
Vol 218 (11) ◽  
pp. 6291-6296 ◽  
Author(s):  
Stevo Stević
Keyword(s):  
Difference Equation ◽  
The Difference

On the difference equation xn+1=α+βxn−1e−xn

2001 ◽  
Vol 47 (7) ◽  
pp. 4623-4634 ◽  
Author(s):  
H. El-Metwally ◽  
E.A. Grove ◽  
G. Ladas ◽  
R. Levins ◽  
M. Radin
Keyword(s):  
Difference Equation ◽  
The Difference

scholarly journals Analytical Study of the Difference Equation xn+1 = xnxn-6 / xn-5 (±1 – xnxn-6)

2019 ◽  
pp. 1-12
Author(s):  
Abdualrazaq Sanbo ◽  
Elsayed M. Elsayed ◽  
Faris Alzahrani
Keyword(s):  
Difference Equation ◽  
Difference Equations ◽  
Analytical Study ◽  
Initial Conditions ◽  
Specific Form ◽  
Positive Real ◽  
Rational Difference Equations ◽  
Special Cases ◽  
The Difference

This paper is devoted to find the form of the solutions of a rational difference equations with arbitrary positive real initial conditions. Specific form of the solutions of two special cases of this equation are given.

Sign in / Sign up

Export Citation Format

Share Document