Fast nearly ML estimation of the parameters of real or complex single tones or resolved multiple tones
- 1 January 1998
- journal article
- Published by Institute of Electrical and Electronics Engineers (IEEE) in IEEE Transactions on Signal Processing
- Vol. 46 (1), 141-148
- https://doi.org/10.1109/78.651200
Abstract
This paper presents new computationally efficient algorithms for estimating the parameters (frequency, amplitude, and phase) of one or more real tones (sinusoids) or complex tones (cisoids) in noise from a block of N uniformly spaced samples. The first algorithm is an interpolator that uses the peak sample in the discrete Fourier spectrum (DFS) of the data and its two neighbors. We derive Cramer-Rao bounds (CRBs) for such interpolators and show that they are very close to the CRB's for the maximum likelihood (ML) estimator. The new algorithm almost reaches these bounds. A second algorithm uses the five DFS samples centered on the peak to produce estimates even closer to ML. Enhancements are presented that maintain nearly ML performance for small values of N. For multiple complex tones with frequency separations of at least 4/spl pi//N rad/sample, unbiased estimates are obtained by incorporating the new single-tone estimators into an iterative "cyclic descent" algorithm, which is a computationally cheap nonlinear optimization. Single or multiple real tones are handled in the same way. The new algorithms are immune to nonzero mean signals and (provided N is large) remain near-optimal in colored and non-Gaussian noise.Keywords
This publication has 19 references indexed in Scilit:
- Thresholds in frequency estimationPublished by Institute of Electrical and Electronics Engineers (IEEE) ,2005
- Estimating frequency by interpolation using Fourier coefficientsIEEE Transactions on Signal Processing, 1994
- Spectral Analysis for Physical ApplicationsPublished by Cambridge University Press (CUP) ,1993
- A fast and accurate single frequency estimatorIEEE Transactions on Acoustics, Speech, and Signal Processing, 1989
- A fast maximum likelihood algorithm for frequency estimation of a sinusoid based on Newton's methodIEEE Transactions on Acoustics, Speech, and Signal Processing, 1985
- Interpolation Algorithms for Discrete Fourier Transforms of Weighted SignalsIEEE Transactions on Instrumentation and Measurement, 1983
- High-Accuracy Analog Measurements via Interpolated FFTIEEE Transactions on Instrumentation and Measurement, 1979
- The estimation of frequencyJournal of Applied Probability, 1973
- On the estimation of a harmonic component in a time series with stationary independent residualsBiometrika, 1971
- Use of the Discrete Fourier Transform in the Measurement of Frequencies and Levels of TonesBell System Technical Journal, 1970