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2022W, 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 of a maximum of three students. 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 6.10.2022, 14:00-15:30 in presence!

## Course dates

DayTimeDateLocationDescription
Thu14:00 - 16:0006.10.2022 - 26.01.2023EI 4 Reithoffer HS Vorlesungs Termine
Fri08:00 - 10:3007.10.2022 - 20.01.2023EI 3A Hörsaal 389.166 Signal Processing 1
Signal Processing 1 - Single appointments
DayDateTimeLocationDescription
Thu06.10.202214:00 - 16:00EI 4 Reithoffer HS Vorlesungs Termine
Fri07.10.202208:00 - 10:30EI 3A Hörsaal 389.166 Signal Processing 1
Thu13.10.202214:00 - 16:00EI 4 Reithoffer HS Vorlesungs Termine
Fri14.10.202208:00 - 10:30EI 3A Hörsaal 389.166 Signal Processing 1
Thu20.10.202214:00 - 16:00EI 4 Reithoffer HS Vorlesungs Termine
Fri21.10.202208:00 - 10:30EI 3A Hörsaal 389.166 Signal Processing 1
Thu27.10.202214:00 - 16:00EI 4 Reithoffer HS Vorlesungs Termine
Fri28.10.202208:00 - 10:30EI 3A Hörsaal 389.166 Signal Processing 1
Thu03.11.202214:00 - 16:00EI 4 Reithoffer HS Vorlesungs Termine
Fri04.11.202208:00 - 10:30EI 3A Hörsaal 389.166 Signal Processing 1
Thu10.11.202214:00 - 16:00EI 4 Reithoffer HS Vorlesungs Termine
Fri11.11.202208:00 - 10:30EI 3A Hörsaal 389.166 Signal Processing 1
Thu17.11.202214:00 - 16:00EI 4 Reithoffer HS Vorlesungs Termine
Fri18.11.202208:00 - 10:30EI 3A Hörsaal 389.166 Signal Processing 1
Thu24.11.202214:00 - 16:00EI 4 Reithoffer HS Vorlesungs Termine
Fri25.11.202208:00 - 10:30EI 3A Hörsaal 389.166 Signal Processing 1
Thu01.12.202214:00 - 16:00EI 4 Reithoffer HS Vorlesungs Termine
Fri02.12.202208:00 - 10:30EI 3A Hörsaal 389.166 Signal Processing 1
Fri09.12.202208:00 - 10:30EI 3A Hörsaal 389.166 Signal Processing 1
Thu15.12.202214:00 - 16:00EI 4 Reithoffer HS Vorlesungs Termine

## Examination modalities

A minimum of 18 points has to be achieved by completing exercises and a midterm exam to be admitted to the final oral exam. The points earned in exercises and midterm are considered in the final grade.

## Exams

DayTimeDateRoomMode of examinationApplication timeApplication modeExam
Thu09:00 - 10:3023.02.2023 Besprechungsraum 313 (CG0313)oral13.01.2023 00:00 - 21.02.2023 09:00TISSOral Exam (presence)
Thu10:45 - 13:0023.02.2023 Besprechungsraum 313 (CG0313)oral13.01.2023 00:00 - 21.02.2023 09:00TISSOral Exam (presence)
Fri11:00 - 12:0024.02.2023 Zoom https://tuwien.zoom.us/j/93146777452oral10.02.2023 08:00 - 20.02.2023 08:00TISSOral Exam (online)
Fri13:00 - 16:0024.02.2023 Zoom https://tuwien.zoom.us/j/93146777452oral10.02.2023 08:00 - 20.02.2023 08:00TISSOral Exam (online)
Wed09:00 - 10:3001.03.2023 Seminar room 402 (CG0402)oral09.01.2023 00:00 - 27.02.2023 12:00TISSOral Exam (presence)
Wed10:45 - 13:0001.03.2023 Seminarraum 402 (CG0402)oral09.01.2023 00:00 - 27.02.2023 12:00TISSOral Exam (presence)

Not necessary

## Literature

Textbook: Moon, Stirling, Mathematical Methods and Algorithms
An additional script including all displayed slides is available from the graphical centre (Graphisches Zentrum)and on TUWEL.

English