The main aim of this book is to introduce different signal processing models which have been used in analyzing periodic data, and different statistical and computational issues. This book discuss in detail the sinusoidal frequency model which has been used extensively in analyzing periodic data occuring in various fields. This book have tried to introduce different associated models and higher dimensional statistical signal processing models which have been further discussed in the literature. Different real data sets have been analyzed to illustrate how different models can be used in practice. Several open problems have been indicated for future research.