Digital Filter Design Using Semidefinite Programming

Examensarbete för kandidatexamen

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Type: Examensarbete för kandidatexamen
Bachelor Thesis
Title: Digital Filter Design Using Semidefinite Programming
Authors: Johansson, Jimmy
Samuelsson, Moa
Samuelsson, Fabian
Abstract: Abstract This thesis explores an optimization based approach to the design problem of digital filters. We show how a digital filter in the form of a discrete linear time-invariant causal system can be characterized by a non-negative trigonometric polynomial, which in turn can be represented by a positive semidefinite matrix known as Gram matrix representation. This allows us to utilize the framework of linear conic optimization, especially semidefinite programming to obtain filters based on given specifications and optimal with respect to some property of the filter. The optimization is carried out with respect to minimizing the stopband energy as well as the passband ripple. We cover both FIR and IIR filters. The model is implemented in MATLAB using the modelling language CVX and solved using SeDuMi.
Keywords: Grundläggande vetenskaper;Matematik;Basic Sciences;Mathematics
Issue Date: 2014
Publisher: Chalmers tekniska högskola / Institutionen för matematiska vetenskaper
Chalmers University of Technology / Department of Mathematical Sciences
Collection:Examensarbeten för kandidatexamen // Bachelor Theses

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