Registration
If you would like to participate in this course, please register via C@mpus.
Please register for both the lecture and the exercise. The lecture and exercise materials can be found in the ILIAS course “Advanced Mathematics for Signal and Information Processing – Exercise”. You should get access to the ILIAS course at the beginning of the lecture period, as long as you have also registered for the exercise in Campus.
Prerequesites
- solid mathematical skills at Bachelor level
- basic knowledge about signals and systems, in particular
- signal and system properties
- LTI system, impulse response, convolution
- Fourier transform, frequency response
Learning Goals
- Learn advanced vector and matrix computations
- Learn probability theory (probability, random variables, stochastic processes)
- Learn the basics of optimization
This course contains the mathematical foundations for all Master courses for signal
and information processing, machine learning and digital communication. It should
be attended first.
Content
- Introduction
- Advanced vector and matrix computations
- Vectors and matrices
- Basic operations
- Determinant and trace
- Vector and matrix norms
- Special vectors and matrices
- Eigenvalue decomposition
- Singular value decomposition
- Rank and subspaces
- Vector and matrix derivatives
- Tensors
- Probability
- Motivation
- Experiment and event
- Probability
- Conditional probability
- Random variables
- Random variable and random vector
- Cumulative distribution function (CDF) and probability density function (PDF)
- Conditional CDF and PDF
- Transformation of random variables
- Expectation and moments
- Moment generating function
- Convergence of a sequence of random variables
- Estimation of statistical properties
- Stochastic processes
- Definition
- CDF and PDF
- Moments
- Stationarity
- Power spectral density
- Estimation of moments and PSD
- Systems with stochastic signals
- System
- Memoryless and time-invariant system
- Linear and time-invariant system
- Introduction to optimization
- Optimization problems
- Optimization conditions
- Optimization algorithms