TTT4120: Digital Signal Processing

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Introduction

Digital Signal Processing is defined as digitalization, processing, transmission and/or representation of physical (analog) signals and modeling of physical signals and systems. The discipline provides methods and algorithms for digitalization and analysis of both physical signals and linear digital systems. It is based on estimation and application of mathematical models.

Typical problems are signal enhancement, interference reduction, efficient coding for transmission or storage, control of industrial process, navigation, classification etc. Within each problem, there may be many applications each requiring solving a variety of problems.

System Identification

Causal and Non Causal Systems

A causal system is a system where the output depends on past and current inputs, but no future inputs i.e the output $ y(t_0) $ only depends on the input $x(t)$ for values of $ t \leq t_0 $.

$$ x(n) = 0, \quad n < 0 $$

Time invariant or time variant

Elementary signals

Unit impulse

$$ \delta(n) = \begin{cases} 1 & , n = 0 \\ 0 & , \text{otherwise} \end{cases} $$

Note that his is the same as the Dirac Pulse as known from calculus.

Unit step

$$ u(n) = \begin{cases} 1 & , n \geq 0 \\ 0 & , \text{otherwise} \end{cases} $$

Also known at the heaviside-function in calculus.

Discrete Time Fourier Transform

Z-transform

Stochastic processes and white noise

Design of FIR- and IIR-filters

Filter implementation

Multirate Signal Processing

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kristiap

Last updated: Thu, 8 Dec 2016 13:15:00 +0100 .