# Chapter five

Discrete models and Z-transforms

## Section one: time series models

This chapter is on the theme of discrete time linear models, for example:

y_{k}+a_{1}y_{k-1} + ...+ a_{n}y_{k-n} = b_{1}u_{k-1} + ...+ b_{n}u_{k-n}

where y(t) is the output, u(t) the input and a_{i }, b_{i} are model parameters. The subscript 'k' denotes the sampling index.

This section focuses on an introduction to time series models, that is models which represent data which changes only at specific instants in time rather than continuously.

### 1. Introduction to time series models

Examples of simple first order time series models from economics and radioactive decay.

Introduction to time series (PDF, 593 KB)

### 2. Modelling from data

Examples of how to estimate the parameters of a simple first order time series model from measured data.

Time series parameters from data (PDF, 608 KB)

### 3. Modelling from data with high order models

Examples of how to estimate the parameters of a high order time series model from measured data using least squares identification methods.

Time series parameters from data (PDF, 572 KB)

Tutorial sheets for chapter five

Online quizzes for chapter five