Digital Filter Design Using Semidefinite Programming
Typ
Examensarbete för kandidatexamen
Bachelor Thesis
Bachelor Thesis
Program
Publicerad
2014
Författare
Johansson, Jimmy
Samuelsson, Moa
Samuelsson, Fabian
Modellbyggare
Tidskriftstitel
ISSN
Volymtitel
Utgivare
Sammanfattning
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.
Beskrivning
Ämne/nyckelord
Grundläggande vetenskaper , Matematik , Basic Sciences , Mathematics