Signal Models and Methods: Parametric vs Nonparametric

This lecture covers the fundamentals of signal models and methods in statistical signal processing. It begins with an introduction to basic signal models, which are categorized into parametric and nonparametric models. The instructor explains the characteristics of nonparametric models, such as independent and identically distributed (i.i.d.) signals, and introduces the concept of wide sense stationary (w.s.s.) processes. The discussion then shifts to parametric models, highlighting the Gaussian process as a key example. The instructor elaborates on the importance of parameters in describing signal behavior and the role of estimation and prediction methods in extracting information from signals. The lecture also addresses the Markov chain model, emphasizing its limited dependence on the past and its characterization through transition probabilities. Finally, the instructor discusses autoregressive (AR) processes, their filtering interpretation, and the synthesis and analysis problems associated with them, providing a comprehensive overview of the methods used in signal processing.