Introduction
As variability and noise affect all measurements, all signals are inherently stochastic variables. Deterministic approaches to signal processing are thus inadequate for many real-world applications. Be it a radar signal to detect a plane, an electrocardiogram to diagnose hearth conditions, or a GPS signal to guide an autonomous car, virtually every engineer deals with real-world signals affected by several sources of noise and interference. Understanding how to handle and process signals in the presence of uncertainty, e.g., “random” signals, is thus fundamental for every student aiming at becoming an engineer. This course provides the basic tools necessary for understanding and processing random signals.
The course is divided into four parts, and it includes a blend of reading and video materials, quizzes, and assignments. The first part covers topics of probability, random variables, and random processes and is a prerequisite for the following parts. The second part dives into estimation theory and methods, including least-square, maximum likelihood, and Bayesian estimation. The third part explains the application of estimation theory in the context of spectral analysis. The final part covers hypothesis testing and detection theory, with applications for detecting a deterministic signal in noise.
Learning goals
At the end of Part 1, students will be able to:
- Understand the basic principles of probability, including probability axioms, independence, conditional probability, Bayes theorem, and use these principles in solving problems.
- Understand and reflect on the implications of the central limit theorem in the context of signal acquisition and analysis.
- Characterize random variables using probability distributions, expected value, variance, and moments.
- Characterize random signals by computing first and second order statistics.
At the end of Part 2, students will be able to:
- Calculate the Cramer-Rao lower bound for the variance of an estimator, given the noise statistics.
- Calculate the bias and variance of an estimator, given the noise statistics.
- Apply the least squares, maximum likelihood, and Bayesian estimations methods to solve problems concerning the estimation of signal model parameters.
- Decide which estimation method to use to solve an estimation problem based on the signal model and availability of noise statistics.
- Apply numerical solution methods to obtain the least-squares and maximum likelihood estimates for problems with nonlinear signal models.
At the end of Part 3, students will be able to:
- Explain the difference between energy and power signals and the implications in the context of real-world signals.
- Describe how windowing and zero-padding affect spectral estimation
- Estimate and analyze the power spectrum of a random signal by applying parametric and non-parametric methods for spectral estimation.
At the end of Part 4, students will be able to:
- Calculate the threshold to achieve a desired false alarm probability and the resulting detection probability based on Neyman-Pearson theorem when given signal statistics for two different hypotheses.
- Plot receiver operating characteristic curves to show the performance of a Neyman-Pearson detector, given signal statistics for two different hypotheses.
- Explain how the Student’s t-test is applied to hypothesis testing.
Study material
The available material consists of:
- Reading material - All required reading material for the course, organized in four different parts, each of which divided in sections.
- Screencast videos - Short informative videos to further explain the subject material. Some of these are addittional, while other are complementary to the reading material.
- Pencast videos - Videos that walk through the solution of selected exercises.
- Quizzes - Short quizzes to test whether you have fully understood the subject matter as explained in the screencast videos.
- Exercises - Homework exercises to help you fully understand the subject matter. Some exercises are part of the student-led tutorial sessions.
- MATLAB labs - Mandatory labs to apply the learned material using MATLAB.
- MATLAB demos - Matlab live scripts to put theoretical knowledge into practice and further enhance your learning experience
Additional reading material
The material covered in this course is based on:
- Steven M. Kay, "Fundamentals of Statistical Signal Processing, Volume I - Estimation Theory" .
- Steven M. Kay, "Fundamentals of Statistical Signal Processing, Volume II - Detection Theory"
- Dimitris G. Manolakis et al. "Statistical and adaptive signal processing"
- Peter M. Clarkson, "Optimal and Adaptive Signal Processing"
- Silvia Maria Alessio, "Digital Signal Processing and Spectral Analysis for Scientists - Concepts and Applications"
We also suggest the following websites:
Planning
A detailed planning for the academic year 2021-22 is available on Canvas.
Contact
In case any of the above material is unclear, please contact the responsible teachers of this course, dr. S. Turco (s.turco@tue.nl) and ir. F. Lampel (f.lampel@tue.nl). If there are any problems with the platform or with the material on the platform, please put the mail address sps.education@tue.nl in the CC of your email, or simply click here. This will help us keep the platform up-to-date.