Introduction

Why this Course?

Goals:

Digital signal processing accounting for the random character of observed real-world signals by evaluating the statistics of the observations.

For this, the observations are described as random (stochastic) processes.

What is Random?

In engineering, the true nature of the world is not considered. Randomness depends on the observer.

Example: Random number generators (RNGs) in computers are deterministic algorithms. Their outputs are not truly random, but they are hard to predict without knowing the internal state or seed.

What is a Statistic and Statistics?

• Statistic: Any quantity computed as a function of given observations (e.g., an arithmetic average)

• Statistics: The mathematical discipline dedicated to computing and analyzing statistics

Why Processing Stochastic Signals?

Only stochastic signals carry information!

Relation to Other Courses

‘StaSiP’ is dedicated to digital signal processing of random signals.

Based on: - Signals and Systems - Basic Probability Theory (from mathematics courses)

Extends: - Stochastic Processes - Digital Signal Processing

Related to: - Information Theory

Contents of the Course

1. Introduction
2. Fundamentals of stochastic processes
3. Introduction to estimation theory
4. Linear signal models
5. Optimum signal estimation
6. Adaptive filtering