## Nonlinear Signal Processing

- Education level
- Master
- Term
- Summer
- Lecturers

## General Description

These two courses combine lectures and problem classes in nonlinear signal processing theory and applications. The theoretical part lays foundations in the area of memoryless nonlinearities (limiters/quantizers/classifiers), nonlinear dynamical systems (nonlinear filters/oscillators/chaos theory), nonlinear statistics (higher-order statistics and information theory), as well as parallel distributed processing (neural networks). The application part is devoted to the modeling of natural signals with nonlinear systems, algorithms for time series analysis and signal synthesis, and nonlinear devices in digital communications systems.

As a prerequisite, students should have prior knowledge in digital signal processing theory and, preferentially, in adaptive systems.

## Lecture course

### Lecture room: HS i12 “INFONOVA Hörsaal” (ICK1130H)

### Lecture dates:

For downloading the lecture slides you need a password. If you have been registered for the course, you should have been received it.

### Exams:

Please consult the TUGonline systems for exam dates.

## Problem classes

The theoretical course is accompanied by practical problem classes. For the problem classes several meetings are planned, spanning four major blocks:

- Median filtering - Introduction into Nonlinear Signal Processing
- Memoryless nonlinearity and Higher Order Statistics (HOS)
- Fading memory systems and the corresponding HOS
- Infinite memory systems (oscillators, chaos ) and information theory

*Grading* is based on four homework assignments, one for each major block. **You are strongly encouraged to work in pairs!** The due date for all four homeworks is **TBA**. Please submit your homeworks at our *mailbox* in Inffeldgasse 16c / ground floor. You can find a map HERE. Please also *submit your code* files to christian.knoll@tugraz.at.

Please use the newsgroup provided by the ZID at *tu-graz.lv.nl-signalprocessing* for discussion of the assignments.

What do you have to submit? A written report (one per group, a group consists of at most 2 students) containing your results, figures and the corresponding discussions for all problems marked with a house icon. For analytic problems you can also hand in hand-written sheets, as long as they are readable. Make sure your report contains enough information such that your results are traceable. Mail your Matlab-files to christian.knoll@tugraz.at. **Take a look** at **and apply** our homework guidelines to avoid unecessary point penalties.

## Problem Classes material

**Important**: Please read and apply our SPSC homework guidelines.

Lesson | Handout | Slides | Files | Sample Solutions |
---|---|---|---|---|

1 - Median Filtering | Handout_1 | Slides_1 | Lesson_1 | SampleSolution_1 |

2 - Static Nonlinearities | Handout_2 | Slides_2 | Lesson_2 | SampleSolution_2 |

3 - Fading Memory Nonlinearities | Handout_3 | Slides_3 | Lesson_3 | SampleSolution_3_1,SampleSolution_3_2 |

4 - Infinite Memory Nonlinearities | Handout_4 | Slides_4 | Lesson_4 | SampleSolution_4, Logistic |