THE ESTIMATION OF PERIODIC SIGNALS IN NOISE
Abstract
The report presents two methods for the estimation of a periodic signal in additive noise. Both methods assume that only a finite time sample of the signal plus noise is available for processing. The estimate of the signal is chosen to minimize the mean square error between the estimate and the sample of signal plus noise. This is also a maximum likelihood estimate if the noise is white and Gaussian. The first method is frequency domain analysis. Estimates for the period of the signal and the complex amplitudes of its harmonics are derived. The second method is time domain analysis. Estimates for the period of the signal and for the waveform of one period are derived. Under the assumption of white noise and large signal-to-noise ratio, formulas for the expected values and variances of the period estimates are derived. The estimates for the period are found to be the same by both methods. The estimate is unbiased and has a variance inversely proportional to the signal-to-noise ratio, and inversely proportional to the cube of the number of periods in the given sample. The expected values of the estimates of the waveform itself are derived, and the estimates are found to be biased.
Document Details
- Document Type
- Technical Report
- Publication Date
- Feb 01, 1968
- Accession Number
- AD0666580
Entities
People
- H. J. Scudder Iii
- T. G. Kincaid
Organizations
- General Electric