## Hans-Andrea Loeliger: Catalogue data in Autumn Semester 2018 |

Name | Prof. Dr. Hans-Andrea Loeliger |

Field | Signalverarbeitung |

Address | Inst. f. Signal-u.Inf.verarbeitung ETH Zürich, ETF E 101 Sternwartstrasse 7 8092 Zürich SWITZERLAND |

Telephone | +41 44 632 27 65 |

loeliger@isi.ee.ethz.ch | |

URL | http://people.ee.ethz.ch/~loeliger/ |

Department | Information Technology and Electrical Engineering |

Relationship | Full Professor |

Number | Title | ECTS | Hours | Lecturers | |
---|---|---|---|---|---|

227-0101-AAL | Discrete-Time and Statistical Signal ProcessingEnrolment ONLY for MSc students with a decree declaring this course unit as an additional admission requirement. Any other students (e.g. incoming exchange students, doctoral students) CANNOT enrol for this course unit. | 6 credits | 8R | H.‑A. Loeliger | |

Abstract | The course introduces some fundamental topics of digital signal processing with a bias towards applications in communications: discrete-time linear filters, equalization, DFT, discrete-time stochastic processes, elements of detection theory and estimation theory, LMMSE estimation and LMMSE filtering, LMS algorithm, Viterbi algorithm. | ||||

Learning objective | The course introduces some fundamental topics of digital signal processing with a bias towards applications in communications. The two main themes are linearity and probability. In the first part of the course, we deepen our understanding of discrete-time linear filters. In the second part of the course, we review the basics of probability theory and discrete-time stochastic processes. We then discuss some basic concepts of detection theory and estimation theory, as well as some practical methods including LMMSE estimation and LMMSE filtering, the LMS algorithm, and the Viterbi algorithm. A recurrent theme throughout the course is the stable and robust "inversion" of a linear filter. | ||||

Content | 1. Discrete-time linear systems and filters: state-space realizations, z-transform and spectrum, decimation and interpolation, digital filter design, stable realizations and robust inversion. 2. The discrete Fourier transform and its use for digital filtering. 3. The statistical perspective: probability, random variables, discrete-time stochastic processes; detection and estimation: MAP, ML, Bayesian MMSE, LMMSE; Wiener filter, LMS adaptive filter, Viterbi algorithm. | ||||

Lecture notes | Lecture Notes. | ||||

227-0101-00L | Discrete-Time and Statistical Signal Processing | 6 credits | 4G | H.‑A. Loeliger | |

Abstract | The course introduces some fundamental topics of digital signal processing with a bias towards applications in communications: discrete-time linear filters, inverse filters and equalization, DFT, discrete-time stochastic processes, elements of detection theory and estimation theory, LMMSE estimation and LMMSE filtering, LMS algorithm, Viterbi algorithm. | ||||

Learning objective | The course introduces some fundamental topics of digital signal processing with a bias towards applications in communications. The two main themes are linearity and probability. In the first part of the course, we deepen our understanding of discrete-time linear filters. In the second part of the course, we review the basics of probability theory and discrete-time stochastic processes. We then discuss some basic concepts of detection theory and estimation theory, as well as some practical methods including LMMSE estimation and LMMSE filtering, the LMS algorithm, and the Viterbi algorithm. A recurrent theme throughout the course is the stable and robust "inversion" of a linear filter. | ||||

Content | 1. Discrete-time linear systems and filters: state-space realizations, z-transform and spectrum, decimation and interpolation, digital filter design, stable realizations and robust inversion. 2. The discrete Fourier transform and its use for digital filtering. 3. The statistical perspective: probability, random variables, discrete-time stochastic processes; detection and estimation: MAP, ML, Bayesian MMSE, LMMSE; Wiener filter, LMS adaptive filter, Viterbi algorithm. | ||||

Lecture notes | Lecture Notes | ||||

227-0427-00L | Signal Analysis, Models, and Machine Learning | 6 credits | 4G | H.‑A. Loeliger | |

Abstract | Mathematical methods in signal processing and machine learning. I. Linear signal representation and approximation: Hilbert spaces, LMMSE estimation, regularization and sparsity. II. Learning linear and nonlinear functions and filters: neural networks, kernel methods. III. Structured statistical models: hidden Markov models, factor graphs, Kalman filter, Gaussian models with sparse events. | ||||

Learning objective | The course is an introduction to some basic topics in signal processing and machine learning. | ||||

Content | Part I - Linear Signal Representation and Approximation: Hilbert spaces, least squares and LMMSE estimation, projection and estimation by linear filtering, learning linear functions and filters, L2 regularization, L1 regularization and sparsity, singular-value decomposition and pseudo-inverse, principal-components analysis. Part II - Learning Nonlinear Functions: fundamentals of learning, neural networks, kernel methods. Part III - Structured Statistical Models and Message Passing Algorithms: hidden Markov models, factor graphs, Gaussian message passing, Kalman filter and recursive least squares, Monte Carlo methods, parameter estimation, expectation maximization, linear Gaussian models with sparse events. | ||||

Lecture notes | Lecture notes. | ||||

Prerequisites / Notice | Prerequisites: - local bachelors: course "Discrete-Time and Statistical Signal Processing" (5. Sem.) - others: solid basics in linear algebra and probability theory |