Numerical Comparison of Five Mean Frequency Estimators

Dale Sirmans National Severe Storms Laboratory, NOAA, Norman, Okla. 73069

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Bill Bumgarner National Severe Storms Laboratory, NOAA, Norman, Okla. 73069

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Abstract

Five techniques of estimating power spectrum mean frequency are examined. Performance is given in terms of estimate bias, accuracy, and noise immunity. Techniques examined are: 1) fast Fourier transform, 2) covariance argument approximation, 3) vector phase change, 4) scalar phase change, and 5) time derivative form of covariance.

Estimator evaluation is made from numerical results obtained with a computer-simulated signal having a Gaussian spectral density which serves as the population with known parameters in the statistical analysis, and 2) real data from a pulsed Doppler radar. Both data sets consist of uniformly time-spaced digital samples of a complex signal. Absolute and relative performance of each estimator are noted, and numerical results are compared with theoretical calculations made by other investigators.

Insofar as the pulsed Doppler meteorological return is represented by the signal type examined (narrow, symmetrical spectral densities), the covariance technique of mean frequency estimation is unbiased and superior in terms of accuracy and noise immunity.

Abstract

Five techniques of estimating power spectrum mean frequency are examined. Performance is given in terms of estimate bias, accuracy, and noise immunity. Techniques examined are: 1) fast Fourier transform, 2) covariance argument approximation, 3) vector phase change, 4) scalar phase change, and 5) time derivative form of covariance.

Estimator evaluation is made from numerical results obtained with a computer-simulated signal having a Gaussian spectral density which serves as the population with known parameters in the statistical analysis, and 2) real data from a pulsed Doppler radar. Both data sets consist of uniformly time-spaced digital samples of a complex signal. Absolute and relative performance of each estimator are noted, and numerical results are compared with theoretical calculations made by other investigators.

Insofar as the pulsed Doppler meteorological return is represented by the signal type examined (narrow, symmetrical spectral densities), the covariance technique of mean frequency estimation is unbiased and superior in terms of accuracy and noise immunity.

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