Estimation of the frequency and decay factor of a decaying exponential in noise

Authors:
Elias Aboutanios
Affiliations:
The School of Electrical Engineering and Telecommunications, The University of New South Wales, Sydney, NSW, Australia
Venue:
IEEE Transactions on Signal Processing
Year:
2010

Citing 5
Cited 2

List of references on spectral line analysis

Signal Processing
Fast nearly ML estimation of the parameters of real or complexsingle tones or resolved multiple tones

IEEE Transactions on Signal Processing
Iterative frequency estimation by interpolation on Fourier coefficients

IEEE Transactions on Signal Processing
Estimation of parameters of exponentially damped sinusoids usingfast maximum likelihood estimation with application to NMR spectroscopydata

IEEE Transactions on Signal Processing
Cramer-Rao lower bounds for a damped sinusoidal process

IEEE Transactions on Signal Processing

Instantaneous frequency based spectral analysis of nuclear magnetic resonance spectroscopy data

Computers and Electrical Engineering
Analytical solutions for frequency estimators by interpolation of DFT coefficients

Signal Processing

Quantified Score

Hi-index	35.68

Visualization

Abstract

In this paper, we examine the estimation of the parameters of a decaying complex exponential in noise. The strategy adopted consists of a computationally simple two stage scheme where an interpolation stage refines the coarse estimate obtained from an initial maximum bin search. The interpolators of Quinn, and of Aboutanios and Mulgrew, developed for undamped exponentials are extended to the damped case. In the process, we show that Quinn's estimator can be viewed as a linearized version of Bertocco's algorithm. Theoretical analysis demonstrates that the resulting estimators exhibit similar behavior to the undamped case, leading us to propose two alternative hybrid implementations that yield a significant improvement in the estimation performance. Unlike the undamped case, however, we show that there exists a finite number of samples for which the estimation performance is best, and which we determine in terms of the damping factor. This enables us to adjust the actual number of samples should it deviate significantly from the optimum. Extensive simulation results are presented to support the theoretical findings.