Random sampling of deterministic signals: Statistical analysis of fourier transform estimates

IEEE Transactions on Signal Processing

Volumn 54, Issue 5, 2006, Pages 1750-1761

  Masry, Elias ^a  

^a UNIVERSITY OF CALIFORNIA   (United States)

Author keywords

Asymptotic normality; Fourier transform; Mean square convergence; Nonuniform sampling; Rates of almost sure convergence; Stratified sampling

Indexed keywords

CONVERGENCE OF NUMERICAL METHODS; ESTIMATION; MATHEMATICAL MODELS; OPTIMIZATION; RANDOM PROCESSES; SAMPLING;

ASYMPTOTIC NORMALITY; MEAN-SQUARE ERRORS; RANDOM SAMPLING ESTIMATES;

FOURIER TRANSFORMS;

EID: 33646069601     PISSN: 1053587X     EISSN: None     Source Type: Journal    
DOI: 10.1109/TSP.2006.872587     Document Type: Article

References (16)

1. A. Antoniou, Digital Filters: Analysis, Design and Applications. New York: McGraw-Hill, 1993.
2. Y. Artyukh, A. Ribakov, and V. Vedin, "Evaluation of pseudorandom sampling processes," in Proc. Workshop Sampling Theory Applications, 1997, pp. 361-363.
3. I. Bilinskis and M. Mikelsons, Randomized Signal Processing. London, U.K.: Prentice-Hall, 1992.
4. I. Bilinskis and M. Mikelsons, "Applications of randomized or irregular sampling as an anti-aliasing technique," in Signal Processing V: Theories and Applications, L. Torres, E. Masgrau, and M. A. Lagunas, Eds. New York: Elsevier, 1990, pp. 357-360.
5. I. Bilinskis and G. D. Cain, "Digital alias-free signal processing in the GHz frequency range," in Inst. Elect. Eng. Colloquium Advanced Signal Processing Microwave Applications, Nov. 1996, Dig. No. 1996/236, pp. 6/1-6/6.
6. D. R. Brillinger, "The spectral analysis of stationary interval functions," in Proc. 6th Berkeley Symp., Probability Statistics, 1972, pp. 83-513.
7. S. Cambanis and E. Masry, "Sampling designs for the detection of signals in noise," IEEE Trans. Inf. Theory, vol. IT-29, no. 1, pp. 83-104, Jan. 1983.
8. M. Loeve, Probability Theory. Princeton, NJ: Van Nostrand, 1963.
9. E. Masry, "Alias free sampling: An alternative conceptualization and its applications," IEEE Trans. Inf. Theory, vol. IT-24, no. 3, pp. 317-324, May 1978.
10. J. M. Hammersley and D. C. Handscomb, The Monte Carlo Method. London, U.K.: Methuen, 1964.
11. E. Masry, "Discrete-time spectral estimation of continuous-time processes - The orthogonal series method," Ann. Stat., vol. 8, pp. 1100-1109, 1980.
12. K. S. Lii and E. Masry, "Spectral estimation of continuous-time stationary processes from random samples," Stoch. Process. Appl., vol. 52, pp. 39-64, 1994.
13. I. Mednieks, "Methods for spectral analysis of non uniformly sampled signals," in Proc. Workshop Sampling Theory Applications, 1999, pp. 190-193.
14. R. J. Serfling, Approximation Theorems of Mathematical Statistics. New York: Wiley, 1980.
15. H. S. Shapiro and R. A. Silverman, "Alias-free sampling of random noise," J. Soc. Indust. A Math., vol. 8, pp. 225-248, 1960.
16. A. Tarczynski and N. Allay, "Spectral analysis of randomly sampled signals: Suppression of aliasing and sampler jitter," IEEE Trans. Signal Process., vol. 52, no. 12, pp. 3324-3334, Dec. 2004.