Cart (Loading....) | Create Account
Close category search window
 

Random sampling of deterministic signals: statistical analysis of Fourier transform estimates

Sign In

Cookies must be enabled to login.After enabling cookies , please use refresh or reload or ctrl+f5 on the browser for the login options.

Formats Non-Member Member
$31 $13
Learn how you can qualify for the best price for this item!
Become an IEEE Member or Subscribe to
IEEE Xplore for exclusive pricing!
close button

puzzle piece

IEEE membership options for an individual and IEEE Xplore subscriptions for an organization offer the most affordable access to essential journal articles, conference papers, standards, eBooks, and eLearning courses.

Learn more about:

IEEE membership

IEEE Xplore subscriptions

1 Author(s)
Masry, E. ; Dept. of Electr. & Comput. Eng., Univ. of California, La Jolla, CA, USA

This paper considers the estimation of the Fourier transform of continuous-time deterministic signals from a finite number N of discrete-time nonuniform observations. We first extend the recent results (mean and variance) of Tarczynski and Allay by providing both distributional properties as well as rates of almost sure convergence for the simple random sampling scheme of Tarczynski and Allay. The primary focus is to consider and investigate the properties of a class of stratified random sampling estimates. We establish the statistical properties of the estimates, including precise expressions and rate of convergence of the mean-square errors. We also establish the asymptotic normality of the estimates useful for confidence interval calculations. Further, we optimize over the class of the estimates in order to obtain the best performance. In particular, we show that for functions with a first-order continuous derivative, the mean-square estimation error decays precisely at the fast rate of 1/N3. This rate is significantly higher than the rate of 1/N for simple random sampling estimates. The analytical results are illustrated by numerical examples. The effect of observation errors on the performance is also investigated.

Published in:

Signal Processing, IEEE Transactions on  (Volume:54 ,  Issue: 5 )

Date of Publication:

May 2006

Need Help?


IEEE Advancing Technology for Humanity About IEEE Xplore | Contact | Help | Terms of Use | Nondiscrimination Policy | Site Map | Privacy & Opting Out of Cookies

A not-for-profit organization, IEEE is the world's largest professional association for the advancement of technology.
© Copyright 2014 IEEE - All rights reserved. Use of this web site signifies your agreement to the terms and conditions.