Statistical signal processing

In this course, the basics of statistical signal processing theory are introduced and some relevant applications in the field of electrical engineering are presented. The course content is organized in three parts:
Part 1 – Brush-up: basic concepts of probability theory, random variables and processes, and their characterization; passage of random signals through linear time-invariant systems; special random processes.
Part 2 – Estimation theory: characterization of estimator performance and bounds; classical estimation by least-square and maximum likelihood approaches; Bayesian estimation, numerical methods for solving estimation problems.
Part 3 - Non-parametric and parametric methods for spectral estimation.
Part 4 – Detection theory: Neyman-Pearson test, Bayesian test, Matched filter.

The course is assessed as follows:
-15% final grade: Lab assignment #1, due date midway the course. Performed in groups of 3-4 students.
-15% final grade: Lab assignment #2, due date at the end of the course. Performed in groups of 3-4 students.
-70% written exam, minimum grade 5.0.
-Mandatory active participation to 4 out 7 instructions. The students (in small groups) need to enroll at least 4 times for a lottery, from which they can be picked to explain to the rest of the classroom the solution to selected exercises.

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.
• Explain the difference between deterministic and stochastic signals providing examples in the context of signal processing.
• 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 sta-tistics.
• 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 es-timates 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 con-text 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 detec-tion probability based on Neyman-Pearson theorem when given signal statistics for two dif-ferent 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

5EMA0 Mathematics II<br> 5ESE0 Signal processing basics (signals I)<br> 5ESC0 DSP Fundamentals (signals II)

• Matlab 2013 / 2014 a en 2014b Matlab (MathWorks ®) – version 2014a or higher
• Fundamentals of Statistical Signal Processing, Vol 1: Estimation Theory. Steven M. Kay, Upper Saddle River, New Jersey, USA: Prentice-Hall, 1993. ISBN-0-13-345711-7
• 5CTA0- Lecture readers, videos and pencasts available on Canvas
• 5CTA0 – Exercise bundle and selected excercises for student-led tutorials, available on Canvas
• 5CTA0 – Lab assignments, available on Canvas