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2018W, VU, 3.0h, 4.5EC

## Properties

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

## Aim of course

To get to know the basics in linear algebra and functional analysis that are relevant for digital signal processing and understand their applications

## Subject of course

1) basics: Notation - Vector, Matrix, Modeling linear Systems, state-space discription, Fourier, Laplace und Z-Transform, sampling theorems

2) Vector spaces and linear algebra: metric spaces, groups, topologic terms, supremum and infimum, series, Cauchy series, linear combinations, lineare independency, basis and dimension, norms and normed vector spaces, inner vector products and inner produkt 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 Filterung, linear regression, Signal transformation and generalized Fourier series, Examples for orthogonal Funktions, 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

oral and written exam

first class: Thu., 4.10.2018, 14:00 - 15:30, EI 3A

There will be no class on 17.1.2019 and 25.1.2019

## Course dates

DayTimeDateLocationDescription
Thu14:00 - 15:3004.10.2018 - 24.01.2019EI 3A Hörsaal 389.166 Signal Processing 1
Fri08:45 - 10:3005.10.2018 - 18.01.2019EI 4 Reithoffer HS 389.166 Signal Processing 1
Signal Processing 1 - Single appointments
DayDateTimeLocationDescription
Thu04.10.201814:00 - 15:30EI 3A Hörsaal 389.166 Signal Processing 1
Fri05.10.201808:45 - 10:30EI 4 Reithoffer HS 389.166 Signal Processing 1
Thu11.10.201814:00 - 15:30EI 3A Hörsaal 389.166 Signal Processing 1
Fri12.10.201808:45 - 10:30EI 4 Reithoffer HS 389.166 Signal Processing 1
Thu18.10.201814:00 - 15:30EI 3A Hörsaal 389.166 Signal Processing 1
Fri19.10.201808:45 - 10:30EI 4 Reithoffer HS 389.166 Signal Processing 1
Thu25.10.201814:00 - 15:30EI 3A Hörsaal 389.166 Signal Processing 1
Thu08.11.201814:00 - 15:30EI 3A Hörsaal 389.166 Signal Processing 1
Fri09.11.201808:45 - 10:30EI 4 Reithoffer HS 389.166 Signal Processing 1
Fri16.11.201808:45 - 10:30EI 4 Reithoffer HS 389.166 Signal Processing 1
Thu22.11.201814:00 - 15:30EI 3A Hörsaal 389.166 Signal Processing 1
Fri23.11.201808:45 - 10:30EI 4 Reithoffer HS 389.166 Signal Processing 1
Thu29.11.201814:00 - 15:30EI 3A Hörsaal 389.166 Signal Processing 1
Fri30.11.201808:45 - 10:30EI 4 Reithoffer HS 389.166 Signal Processing 1
Thu06.12.201814:00 - 15:30EI 3A Hörsaal 389.166 Signal Processing 1
Fri07.12.201808:45 - 10:30EI 4 Reithoffer HS 389.166 Signal Processing 1
Thu13.12.201814:00 - 15:30EI 3A Hörsaal 389.166 Signal Processing 1
Fri14.12.201808:45 - 10:30EI 4 Reithoffer HS 389.166 Signal Processing 1
Thu20.12.201814:00 - 15:30EI 3A Hörsaal 389.166 Signal Processing 1
Fri21.12.201808:45 - 10:30EI 4 Reithoffer HS 389.166 Signal Processing 1

## Exams

DayTimeDateRoomMode of examinationApplication timeApplication modeExam
Fri09:00 - 14:0028.02.2020 CG0402oral01.01.2020 08:00 - 26.02.2020 08:00TISSSP1 Oral Exam
Wed08:00 - 13:0004.03.2020 CG0402oral01.01.2020 08:00 - 02.03.2020 08:00TISSSP1 Oral Exam

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