NDLI: Random Sampling Estimates of Fourier Transforms: Antithetical Stratified Monte Carlo

Content Provider	IEEE Xplore Digital Library
Author	Masry, E. Vadrevu, A.
Copyright Year	1991
Abstract	We estimate the Fourier transform of continuous-time signals on the basis of N discrete-time nonuniform observations. We introduce a class of antithetical stratified random sampling schemes and we obtain the performance of the corresponding estimates. We show that when the underlying function f(t) has a continuous second-order derivative, the rate of mean square convergence is 1/N ⁵, which is considerably faster that the rate of 1/N ³ for stratified sampling and the rate of 1/N for standard Monte Carlo integration. In addition, we establish joint asymptotic normality for the real and imaginary parts of the estimate and give an explicit expression for the asymptotic covariance matrix. The theoretical results are illustrated by examples for low-pass and high-pass signals.
Sponsorship	IEEE Signal Processing Society
Starting Page	194
Ending Page	204
Page Count	11
File Size	766831
File Format	PDF
ISSN	1053587X
Volume Number	57
Issue Number	1
Language	English
Publisher	Institute of Electrical and Electronics Engineers, Inc. (IEEE)
Publisher Date	2009-01-01
Publisher Place	U.S.A.
Access Restriction	One Nation One Subscription (ONOS)
Rights Holder	Institute of Electrical and Electronics Engineers, Inc. (IEEE)
Subject Keyword	Sampling methods Fourier transforms Monte Carlo methods Convergence Estimation error Covariance matrix Random processes Frequency estimation Nonuniform sampling Signal sampling nonuniform sampling Asymptotic normality Fourier transforms estimates mean-square convergence
Content Type	Text
Resource Type	Article
Subject	Signal Processing Electrical and Electronic Engineering

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