# 389.166 Signal Processing 1 This course is in all assigned curricula part of the STEOP.\$(function(){PrimeFaces.cw("Tooltip","widget_j_id_20",{id:"j_id_20",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_22",{id:"j_id_22",showEffect:"fade",hideEffect:"fade",target:"isAnySteop"});}); 2021W 2020W 2019W 2018W 2017W 2016W 2015W 2014W 2013W

2020W, VU, 3.0h, 4.5EC

## Properties

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

## Learning outcomes

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

## Subject of course

1) Basics: Notation - Vector, Matrix, Modeling linear Systems, state-space discription, 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 independency, 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 im 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 sub spaces, 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, Overlab add and save Methods, circulant matrices, examples to OFDM, Vec-Operator, Big Data, asymptotic equivalence of Toeplitz and circulant matrices.

Textbook: Moon, Stirling, Mathematical Methods and Algorithms

An addional script together with a copy of the presented slides is available in the graphical center

## Teaching methods

Methods of linear algebra as should be known from the bachelor studies are formally applied to describe signals and systems.

## Mode of examination

Written and oral

oral and written exam

first class: Thu., 1.10.2020, 14:00 - 15:30,

via Zoom

https://tuwien.zoom.us/j/92597078196?pwd=alVPQk4wQll3TnBRUFFtNWIvT3Y5Zz09

Meeting ID: 925 9707 8196

After that no presentation in room.

All lectures will be provided with audio taping.

There will be opportunities to listen in to life streams as the lecture is also offered to students at TU Brno. first 24.9 at 9am.

## Course dates

DayTimeDateLocationDescription
Thu14:00 - 16:0001.10.2020 - 21.01.2021EI 3A Hörsaal 389.166 Signal Processing 1
Fri08:00 - 10:3002.10.2020 - 15.01.2021EI 4 Reithoffer HS - ETIT 389.166 Signal Processing 1
Thu14:00 - 17:3017.12.2020EI 5 Hochenegg HS - ARCH/INF 389.166 Signal Processing 1 (SP1), Midterm
Signal Processing 1 - Single appointments
DayDateTimeLocationDescription
Fri02.10.202008:00 - 10:30EI 4 Reithoffer HS - ETIT 389.166 Signal Processing 1
Fri09.10.202008:00 - 10:30EI 4 Reithoffer HS - ETIT 389.166 Signal Processing 1
Fri16.10.202008:00 - 10:30EI 4 Reithoffer HS - ETIT 389.166 Signal Processing 1
Fri23.10.202008:00 - 10:30EI 4 Reithoffer HS - ETIT 389.166 Signal Processing 1
Fri30.10.202008:00 - 10:30EI 4 Reithoffer HS - ETIT 389.166 Signal Processing 1
Fri06.11.202008:00 - 10:30EI 4 Reithoffer HS - ETIT 389.166 Signal Processing 1
Fri13.11.202008:00 - 10:30EI 4 Reithoffer HS - ETIT 389.166 Signal Processing 1
Fri20.11.202008:00 - 10:30EI 4 Reithoffer HS - ETIT 389.166 Signal Processing 1
Fri27.11.202008:00 - 10:30EI 4 Reithoffer HS - ETIT 389.166 Signal Processing 1
Fri04.12.202008:00 - 10:30EI 4 Reithoffer HS - ETIT 389.166 Signal Processing 1
Fri11.12.202008:00 - 10:30EI 4 Reithoffer HS - ETIT 389.166 Signal Processing 1
Fri18.12.202008:00 - 10:30EI 4 Reithoffer HS - ETIT 389.166 Signal Processing 1
Fri08.01.202108:00 - 10:30EI 4 Reithoffer HS - ETIT 389.166 Signal Processing 1
Fri15.01.202108:00 - 10:30EI 4 Reithoffer HS - ETIT 389.166 Signal Processing 1

## Examination modalities

Home exercises and midterm are required for a minimum score (18p). After that, acceptance to the oral exam is given. Performance at the exercises and midterm is taken into account for the final scoring.

## Exams

DayTimeDateRoomMode of examinationApplication timeApplication modeExam
Fri15:00 - 18:0017.12.2021EI 3 Sahulka HS - RPL written29.11.2021 00:00 - 10.12.2021 00:00TISSschriftl. Prüfung

Not necessary

## Literature

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

## Previous knowledge

Mathematically oriented part of bacc studies is assumed to be passed! For example, Math I-III, Signals and Systems I and II, Electrodynamics

English