Statistical Signal Processing in Engineering

5Models and Applications

This chapter introduces some simple models and applications that will provide a set of concrete examples for the dissertation of the estimation methods. Any data¹ should be modeled by a set of parameters, and the estimation problem reduces to getting the “best set of parameters” describing these data. But a first step is the understanding of the generation mechanism of the data and their representation; this is referred as data (or experiment) modeling, or simply model definition.

In signal processing, applications where the data is affected by additive noise is very common, and intuitive. The ith observation

is the sum of a term of interest s[i; θ] (signal) that depends on a set of parameters (or in general ) such that (admissible set), and an additive random term w(i) that is commonly referred as noise. Multiple observations are used to estimate the set of parameters θ, these are ordered in a vector/matrix form (except for time series where the ordering ...