Simple test for distinguishing constant from time-varying amplitude in harmonic retrieval

In many harmonic retrieval problems, it is not known a priori whether the a mplitude of the sinusoidal signals dealt with is constant or time varying. In such applications, a key problem, prior to or in conjunction with freque ncy estimation, is to decide between these two alternatives or hypotheses. In this correspondence, a statistical test for this Problem is derived, bas ed 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. Numerical examples are include d to show the performance of the proposed test.