Langname	Digital Signal Processing
Anerkennende LModule	DSP_MaCSN, DSP_MaTIN
Verantwortlich	Prof. Dr. Harald Elders-Boll Professor Fakultät IME
Niveau	Master
Semester im Jahr	Wintersemester
Dauer	Semester
Stunden im Selbststudium	60
ECTS	5
Dozenten	Prof. Dr. Harald Elders-Boll Professor Fakultät IME
Voraussetzungen	No formal requirements, but students will be expected to be familiar with: Basic Knowledge of Signals and Systems: Continuous-Time LTI-Systems and Convolution, Fourier-Transform Basic Knowledge of Probability and Random Variables
Unterrichtssprache	englisch
separate Abschlussprüfung	Ja

Signals, Systems and Digital Signal Processing
Basic Elements of DSP Systems
Classification of Signals
Continuous-Time and Discrete-Time Signals
Deterministic and Random Signals
Even and Odd Signals
Periodic and Aperiodic Signals
Energy and Power of Signals
Some Fundamental Signals

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Discrete-Time Linear Time-Invariant Systems
Difference Equations
Discrete-Time Convolution
Unit-Pulse and Impulse Response
Basic Systems Properties: Causality, Stability, Memory

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Ideal Sampling and Reconstruction
Ideal Sampling and the Sampling Theorem
Aliasing

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Fourier-Transform of Discrete-Time Signals
Eigenfunctions of Discrete-Time LTI Systems
Frequency response of Discrete-Time LTI Systems
The Fourier-Transform of Discrete-Time Signals
Ideal Continuous-Time Filters

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The z-Transform
The Two-sided z-Transform
Properties of the z-Transform
The Inverse z-Transform
Analysis of LTI Systems using the z-Transform

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Discrete Fourier-Transform
Sampling the DTFT
The DFT and the Inverse DFT
The Fast Fourier Transform
Radix-2 FFT Algorithms
Linear Convolution Using the FFT
Overlap-And-Add

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Design of Digital Filters
Design of FIR Filters
Design of IIR Filters

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Random Signals
Review of Probablity and Random Variables
Ensemble Averages
Correlation Functions
Stationary and Ergodic Processes
Power Spectral Density
Transmission of Random Signals over LTI Systems

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Advanced Sampling Techniques
Quantization and Encoding
Sampling of Bandpass Signals
Sampling of Random Signals
Sample Rate Conversion
Sample Rate Reduction by an Integer Factor
Sample Rate Increase by an Integer Factor
Sample Rate Conversion by a Rational Factor
Oversampling and Noise Shaping

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Optimum Linear Filters
Linear Prediction
The Wiener Filter
Orthogonality Principle
FIR Wiener Filter
IIR Wiener Filter

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Spectrum Estimation
The Periodogram
Window Functions
Eigenanalysis Algorithms
MUSIC Algorithm
ESPRIT Algorithm

Students understand the fundamentals of discrete-time signals and systems

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Students can analyse the frequency content of a given signal using the appropriate Fourier-Transform and methods for spectrum estimation

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Analysis of discrete-time LTI Systems
Students can calculate the output signal via convolution
Students can determine the frequency response of a given system
Students can characterize a given system in the frequency domain and in the z-domain

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Implementation of discrete-time LTI systems
Students can implement the convolution sum in software
Students can implement different structures for IIR systems in software
Sudents can use the FFT to implement an FIR system

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Analyze effects of practical sampling
Quantization noise
Aliasing
Trade-off pros and cons of advanced implementations like noise shaping

Typ	Präsenzzeit (h/Wo.)
Vorlesung	2
Übungen (ganzer Kurs)	2
Übungen (geteilter Kurs)	0
Tutorium (freiwillig)	0

Review of Probablity and Random Variables
Moments, Averages and Distribution Functions

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Random Signals
Ensemble Averages
Correlation Functions
Stationary and Ergodic Processes
Power Spectral Density
Transmission of Random Signals over LTI Systems

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Sampling
Sampling and coding for speech and/or audio signals

Analysis of random variables by means of
Mean and moments
Distribution

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Analysis of random signals
Determine whether a given random signal is stationary or not
Analyse whether a random signal contains discrete harmonic components
by using the autocorrelation function
by using the power spectral density

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Combatting noise
Remove or suppress high-frequency noise from low-pass signals

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Abilty to trade-off different methods for digital coding of speech and audio signals

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Determine the quatization noise and the SNR for different sampling schemes

Typ	Präsenzzeit (h/Wo.)
Praktikum	1
Tutorium (freiwillig)	0