Title :
Statistical Analysis of Fourier Transform Estimates: Monte Carlo and Stratified Sampling
Author_Institution :
Electr. & Comput. Eng., California Univ., San Diego, La Jolla, CA
Abstract :
We consider the estimation of the Fourier transform of continuous-time deterministic signals from a finite number N of discrete-time non-uniform observations. The primary focus is to investigate the properties of a class stratified random sampling estimates. We obtain the statistical properties of the estimates including precise expressions and rate of convergence of the mean-square errors. We also optimize over the class 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 first rate of 1/N3. This rate is significantly higher than the rate of 1/N for standard Monte Carlo. The analytical results are illustrated by numerical examples
Keywords :
Fourier transforms; Monte Carlo methods; mean square error methods; signal sampling; Fourier transform estimates; Monte Carlo; continuous-time deterministic signals; discrete-time nonuniform observations; mean-square errors; statistical analysis; statistical properties; stratified random sampling estimates; Convergence; Fourier transforms; Frequency estimation; Information technology; Monte Carlo methods; Sampling methods; Signal processing; Signal sampling; Statistical analysis; USA Councils; Fourier tranfonn; asymptotic normality; mean-square convergence; nonuniform sampling; rates of almost sure convergence; stratified sampling;
Conference_Titel :
Signal Processing and Information Technology, 2006 IEEE International Symposium on
Conference_Location :
Vancouver, BC
Print_ISBN :
0-7803-9753-3
DOI :
10.1109/ISSPIT.2006.270896