NDLI: Some Studies on the Structure of Covariance Matrix of Discrete-Time fBm

Content Provider	IEEE Xplore Digital Library
Author	Gupta, A. Joshi, S.
Copyright Year	1991
Abstract	This paper presents some results on the structure of autocovariance matrix of discrete-time fractional Brownian motion. Since these processes are nonstationary, the autocovariance matrix is a function of time. The eigenvalues associated with the autocovariance matrix are dependent on Hurst exponent characterizing the discrete-time fractional Brownian motion. However, it is seen that only one eigenvalue of this autocovariance matrix depends on time index n in the asymptotic sense, and it increases as the time index increases. All other eigenvalues are observed to be invariant with time index in the asymptotic sense. It is observed that the eigenvectors associated with these eigenvalues have an interesting structure and these eigenvectors can be used as filters of an M-band orthogonal wavelet system. The eigenvector associated with the time-varying eigenvalue is a lowpass filter. The subband signal from this lowpass filtered branch imbibes the nonstationary attribute of the input process and is a nonstationary signal whereas all other subband signals are stationary in nature.
Sponsorship	IEEE Signal Processing Society
Starting Page	4635
Ending Page	4650
Page Count	16
File Size	1051079
File Format	PDF
ISSN	1053587X
Volume Number	56
Issue Number	10
Language	English
Publisher	Institute of Electrical and Electronics Engineers, Inc. (IEEE)
Publisher Date	2008-10-01
Publisher Place	U.S.A.
Access Restriction	One Nation One Subscription (ONOS)
Rights Holder	Institute of Electrical and Electronics Engineers, Inc. (IEEE)
Subject Keyword	Covariance matrix Brownian motion Signal processing Eigenvalues and eigenfunctions Random processes Wavelet analysis Filters Wavelet transforms Image texture analysis Fractals wavelet transforms Discrete-time fractional Brownian motion (dfBm) fractals modeling Discrete-time fractional Brownian motion
Content Type	Text
Resource Type	Article
Subject	Signal Processing Electrical and Electronic Engineering

Sl.	Authority	Responsibilities	Communication Details
1	Ministry of Education (GoI), Department of Higher Education	Sanctioning Authority	https://www.education.gov.in/ict-initiatives
2	Indian Institute of Technology Kharagpur	Host Institute of the Project: The host institute of the project is responsible for providing infrastructure support and hosting the project	https://www.iitkgp.ac.in
3	National Digital Library of India Office, Indian Institute of Technology Kharagpur	The administrative and infrastructural headquarters of the project	Dr. B. Sutradhar bsutra@ndl.gov.in
4	Project PI / Joint PI	Principal Investigator and Joint Principal Investigators of the project	Dr. B. Sutradhar bsutra@ndl.gov.in Prof. Saswat Chakrabarti will be added soon
5	Website/Portal (Helpdesk)	Queries regarding NDLI and its services	support@ndl.gov.in
6	Contents and Copyright Issues	Queries related to content curation and copyright issues	content@ndl.gov.in
7	National Digital Library of India Club (NDLI Club)	Queries related to NDLI Club formation, support, user awareness program, seminar/symposium, collaboration, social media, promotion, and outreach	clubsupport@ndl.gov.in
8	Digital Preservation Centre (DPC)	Assistance with digitizing and archiving copyright-free printed books	dpc@ndl.gov.in
9	IDR Setup or Support	Queries related to establishment and support of Institutional Digital Repository (IDR) and IDR workshops	idr@ndl.gov.in

PCA Based Hurst Exponent Estimator for fBm Signals Under Disturbances

The ergodicity analysis of two-dimensional discrete wavelet-based fBm fields

Wavelet analysis and synthesis of fractional Brownian motion

A novel wavelet-based generalized sidelobe canceller

On the correlation structure of the wavelet coefficients of fractional Brownian motion

The wavelet transform of stochastic processes with stationary increments and its application to fractional Brownian motion

Wavelet Packets of Fractional Brownian Motion: Asymptotic Analysis and Spectrum Estimation

On the continuous wavelet transform of second-order random processes

Generalized Morse wavelets

Some Studies on the Structure of Covariance Matrix of Discrete-Time fBm

Similar Documents

PCA Based Hurst Exponent Estimator for fBm Signals Under Disturbances

The ergodicity analysis of two-dimensional discrete wavelet-based fBm fields

Wavelet analysis and synthesis of fractional Brownian motion

A novel wavelet-based generalized sidelobe canceller

On the correlation structure of the wavelet coefficients of fractional Brownian motion

The wavelet transform of stochastic processes with stationary increments and its application to fractional Brownian motion

Wavelet Packets of Fractional Brownian Motion: Asymptotic Analysis and Spectrum Estimation

On the continuous wavelet transform of second-order random processes

Generalized Morse wavelets

Some Studies on the Structure of Covariance Matrix of Discrete-Time fBm