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

In many harmonic retrieval problems, it is not known a priori whether the amplitude of the sinusoidal signals dealt with is constant or time varying. In such applications, a key problem, prior to or in conjunction with frequency estimation, is to decide between these two alternatives or hypotheses. A statistical test for this problem is derived, 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. Numerical examples are included to show the performance of the proposed test