Sinteza IIR Hilbertovih transformatora u vremenskoj domeni

scientific master's theses

• Title (english): Time-domain synthesis of IIR Hilbert transformers
• Author: Aleksandar Ljutić
• Mentor: Mladen Vučić (mentor)
• Committee member: Davor Petrinović (predsjednik povjerenstva)
• Committee member: Mladen Vučić (član povjerenstva)
• Committee member: Miroslav Vrankić (član povjerenstva)
• Granter: University of Zagreb; Faculty of Electrical Engineering and Computing; (Department of Electronic Systems and Information Processing); Zagreb
• Defense date and country: 2011-11-24, Croatia
• Scientific / art field, discipline and subdiscipline: TECHNICAL SCIENCES; Electrical Engineering
• Universal decimal classification (UDC): 621.3 - Electrical engineering

Abstract

Klasičan pristup sintezi sustava od kojih se zahtijevaju mala izobličenja vremenskih odziva temelji se na zahtjevu za linearnom fazom koja se zatim aproksimira. Ovakav pristup je neizravan. Bolji rezultati mogu se očekivati ako se prijenosna funkcija sustava odredi na temelju zahtjeva zadanih u vremenskoj domeni. Jedan ovakav pristup temelji se na simetriji vremenskog odziva. Hilbertov transformator je fazni zakretač s jediničnom amplitudnom karakteristikom. Tradicionalno se njegova sinteza provodi u frekvencijskoj domeni. S druge strane, poznato je da je vremenski odziv konvencionalnog Hilbertovog transformatora na parno simetričnu pobudu neparno simetričan. Ovo svojstvo može se iskoristiti kao kriterij za sintezu u vremenskoj domeni, što je opisano u dosadašnjoj literaturi. U ovom radu predložena je metoda za sintezu frakcionalnih Hilbertovih transformatora u vremenskoj domeni. Kao model ulaznog signala korišten je sinc puls zadane faze. Mjera izobličenja definirana je pomoću simetrije dobivenog odziva. Numeričkom optimizacijom ove mjere dobiveni su optimalni frakcionalni Hilbertovi transformatori. U radu su razmatrani rekurzivni svepropusni transformatori. Za njih je simetrija odziva određena u analitičkom obliku, čime je osigurana velika robusnost optimizacijskog postupka. Kao primjer opisana je jedna klasa dobivenih transformatora, te su dani parametri njihovih prijenosnih funkcija.

Abstract (english)

Classical approach in filter design, when a small time domain signal distorsion is required, is based on linear phase criterion which is approximated. This is indirect approach. One should expect better results if transfer function based on time-domain criteria is determined. The following approach is based on time-domain response symmetry. Hilbert transformer is a phase shifter with unity magnitude response. Traditionally it is designed in frequency domain. On the other hand, it is known that conventional Hilbert transformer on even-symmetric excitation signal gives odd-symmetric time-domain response. This characteristic can be used as time-domain synthesis criterion which is described in existing literature. In this paper, a method for fractional Hilbert transformer design is determined. As excitation signal model sinc pulse with given phase is used. The measure of distorsion is defined by symmetry of obtained response. Optimal fractional Hilbert transformers are obtained by numerical optimization of this measure. In this paper, recursive all-pass transformers are considered. For them response symmetry is determined in analytical form, whereby optimization method robustness is ensured. As an example, a new class of obtained fractional Hilbert transformers is described, and parameters of their transfer functions are also given.

• Keywords: konvencionalni Hilbertov transformator; frakcionalni Hilbertov transformator; sinteza u vremenskoj domeni; simetrija vremenskog odziva; numerička optimizacija
• Keywords (english): conventional Hilbert transformer; fractional Hilbert transformer; time-domain synthesis; time-domain response symmetry; numerical optimization
• Language: croatian
• URN:NBN: urn:nbn:hr:168:173339
• Project: Number: 036-0362214-2217; Title: Razvoj i implementacija učinkovitih postupaka za digitalnu obradu signala; Leader: Mladen Vučić; Jurisdiction: Croatia; Funder: MZOS; Funding stream: ZP
• Study programme: Title: Postgraduate master programme in electrical engineering; Study programme type: university; Study level: postgraduate; Academic / professional title: Magistar znanosti elektrotehnike (Magistar znanosti elektrotehnike)
• Catalog URL: http://lib.fer.hr/cgi-bin/koha/opac-detail.pl?biblionumber=36998
• Type of resource: Text
• Extent: 96 str ; 30 cm
• File origin: Born digital
• Access conditions: Closed access
• Created on: 2020-08-26 08:16:57