# 389.166 Signal Processing 1 This course is in all assigned curricula part of the STEOP.\$(function(){PrimeFaces.cw("Tooltip","widget_j_id_21",{id:"j_id_21",showEffect:"fade",hideEffect:"fade",target:"isAllSteop"});});This course is in at least 1 assigned curriculum part of the STEOP.\$(function(){PrimeFaces.cw("Tooltip","widget_j_id_23",{id:"j_id_23",showEffect:"fade",hideEffect:"fade",target:"isAnySteop"});}); 2023W 2022W 2021W 2020W 2019W 2018W 2017W 2016W 2015W 2014W 2013W

2023W, VU, 3.0h, 4.5EC

## Properties

• Semester hours: 3.0
• Credits: 4.5
• Type: VU Lecture and Exercise
• Format: Presence

## Learning outcomes

After successful completion of the course, students are able to understand digital signal processing on an elevated level, apply modern methods of linear algebra to process signals, and follow recent literature in this field.

## Subject of course

1) Basics: Notation - Vector, Matrix, Modeling linear Systems, state-space description, Fourier, Laplace, and Z-Transform, sampling theorems

2) Vector spaces and linear algebra: metric spaces, groups, topologic terms, supremum and infimum, series, Cauchy series, linear combinations, linear independence, basis and dimension, norms and normed vector spaces, inner vector products and inner product spaces, Induced norms and Cauchy-Schwarz Inequality, Orthogonality, Hilbert and Banach spaces,

3) Representation and Approximation in Vector spaces: Approximation problem in Hilbert space, Orthogonality principle, Minimisation with gradient method, Least Square Filtering, linear regression, machine learning, Signal transformation and generalized Fourier series, Examples for orthogonal Functions, Wavelet

4) Linear Operators: Linear Functionals, norms on Operators, Orthogonal subspaces, null space and Range, Projections, Adjoint Operators, Matrix rank, Inverse and condition number, matrix decompositions, subspace methods: Pisarenko, music, esprit, singular value decomposition.

5) Kronecker Products: Kronecker Products and Sums, DFT, FFT, Hadamard Transformations, Special Forms of FFT, Split Radix FFT, Overlap add and save Methods, circulant matrices, examples to OFDM, Vec-Operator, Big Data, asymptotic equivalence of Toeplitz and circulant matrices

## Teaching methods

The understanding of the contents of the lecture is deepened with calculation exercises that have to be solved at home and handed in for correction. The solved exercises are also presented on the blackboard. Additionally, python programming exercises have to be solved in groups. The solution to the python exercises is also handed in, corrected, and presented.

## Mode of examination

Written and oral

The lecture is held in presence if possible.

First lecture: Thursday 5.10.2023, 14:00-15:30 in presence!

## Course dates

DayTimeDateLocationDescription
Thu14:00 - 16:0005.10.2023 - 25.01.2024EI 4 Reithoffer HS Vorlesungs Termine
Fri08:00 - 10:3006.10.2023 - 19.01.2024EI 3A Hörsaal 389.166 Signal Processing 1
Signal Processing 1 - Single appointments
DayDateTimeLocationDescription
Thu05.10.202314:00 - 16:00EI 4 Reithoffer HS Vorlesungs Termine
Fri06.10.202308:00 - 10:30EI 3A Hörsaal 389.166 Signal Processing 1
Thu12.10.202314:00 - 16:00EI 4 Reithoffer HS Vorlesungs Termine
Fri13.10.202308:00 - 10:30EI 3A Hörsaal 389.166 Signal Processing 1
Thu19.10.202314:00 - 16:00EI 4 Reithoffer HS Vorlesungs Termine
Fri20.10.202308:00 - 10:30EI 3A Hörsaal 389.166 Signal Processing 1
Fri27.10.202308:00 - 10:30EI 3A Hörsaal 389.166 Signal Processing 1
Fri03.11.202308:00 - 10:30EI 3A Hörsaal 389.166 Signal Processing 1
Thu09.11.202314:00 - 16:00EI 4 Reithoffer HS Vorlesungs Termine
Fri10.11.202308:00 - 10:30EI 3A Hörsaal 389.166 Signal Processing 1
Thu16.11.202314:00 - 16:00EI 4 Reithoffer HS Vorlesungs Termine
Fri17.11.202308:00 - 10:30EI 3A Hörsaal 389.166 Signal Processing 1
Thu23.11.202314:00 - 16:00EI 4 Reithoffer HS Vorlesungs Termine
Fri24.11.202308:00 - 10:30EI 3A Hörsaal 389.166 Signal Processing 1
Thu30.11.202314:00 - 16:00EI 4 Reithoffer HS Vorlesungs Termine
Fri01.12.202308:00 - 10:30EI 3A Hörsaal 389.166 Signal Processing 1
Thu07.12.202314:00 - 16:00EI 4 Reithoffer HS Vorlesungs Termine
Thu14.12.202314:00 - 16:00EI 4 Reithoffer HS Vorlesungs Termine
Fri15.12.202308:00 - 10:30EI 3A Hörsaal 389.166 Signal Processing 1
Thu21.12.202314:00 - 16:00EI 4 Reithoffer HS Vorlesungs Termine

## Examination modalities

The achievable points are distributed as follows:

• 13.5 calculus exercise
• 6 python exercise in group
• 4.5 blackboard presentation
• 15 midterm exam
• 67 oral exam

A minimum of 18 points has to be achieved by completing exercises and a midterm exam to be admitted to the final oral exam. At least 40 points have to be achieved to pass the course.

## Exams

DayTimeDateRoomMode of examinationApplication timeApplication modeExam
Thu14:00 - 18:0014.12.2023EI 4 Reithoffer HS written15.11.2023 08:00 - 13.12.2023 08:00TISSMidterm

Not necessary

## Curricula

Study CodeObligationSemesterPrecon.Info
066 504 Master programme Embedded Systems Not specified
066 506 Energy Systems and Automation Technology Mandatory elective
066 507 Telecommunications Not specified1. Semester
066 515 Automation and Robotic Systems Not specified
066 938 Computer Engineering Mandatory elective

## Literature

Lecture notes and slides are available on TUWEL. A printed version of the lecture notes including all displayed slides is available at the graphical centre (Graphisches Zentrum). Should there be no more copies left, then please contact us and we will put some in production.
Additionally the following textbook is recommended: Moon, Stirling, Mathematical Methods and Algorithms

English