Frequency estimation and detection for sinusoidal signals with arbitrary envelope: a nonlinear least-squares approach

In this paper, we consider the problem of estimating the frequency of a sinusoidal signal whose amplitude could be either constant or time-varying. We present a nonlinear least-squares (NLS) approach when the envelope is time-varying. We show that the NLS estimator can be efficiently implemented using a FFT. A statistical analysis shows that the NLS frequency estimator is nearly efficient. The problem of detecting amplitude time variations is next addressed. A statistical test is formulated, based on the statistics of the difference between two frequency estimates. The test is computationally efficient and yields as a by-product consistent frequency estimates under either hypothesis (i.e. constant or time-varying amplitude). Numerical examples are included to show the performance in terms of both estimation and detection