Nonlinear least-squares approach to frequency estimation and detection forsinusoidal signals with arbitrary envelope

In this paper, we consider the problem of estimating the frequency of a sin usoidal signal whose amplitude could be either constant or time-varying. We present a nonlinear least-squares (NLS) approach when the envelope is time -varying. It is shown that the NLS criterion can be explicitly minimized wi th respect to the signal amplitude and envelope values, leaving out a perio dogram-like function whose peak location gives the frequency estimate. This result is a significant generalization of a similar result on the NLS freq uency estimation for a sinusoidal signal with constant amplitude. A statist ical analysis shows that the NLS frequency estimator is asymptotically stat istically efficient. The problem of detecting amplitude time variations is next addressed. A statistical test is formulated, based on the statistics o f the difference between two frequency estimates. The test is computational ly efficient and yields as a by-product consistent frequency estimates unde r either hypothesis (i.e., constant or time-varying amplitude). Numerical e xamples are included to show the performance both in terms of estimation an d detection. (C) 1999 Academic Press.