The sinusoidal frequency model is a well-known model in different fields of science and technology and as has been observed in previous chapters, it is a very useful model for explaining nearly periodical data. There are several other models which are practically the multiple sinusoidal model, but also exploit some extra features in the data. In most of such cases, the parameters satisfy some additional conditions other than the assumptions required for the sinusoidal model. For example, if the frequencies appear at \(\lambda , 2\lambda , \ldots , p\lambda \) in a multiple sinusoidal model, then the model that exploits this extra information is the fundamental frequency model. The advantage of using this information in the model itself is that it reduces the total number of parameters to \(2p+1\) from \(3p\) and a single non-linear parameter instead of \(p\), in case of multiple sinusoidal model. Similarly, if the gap between two consecutive frequencies is approximately same, then the suitable model is the generalized fundamental frequency model. We call these models as “related models” of the sinusoidal frequency model.
KeywordsFundamental Frequency Asymptotic Variance Strong Consistency Frequency Model Sinusoidal Component
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