Banca de QUALIFICAÇÃO: EULOGIO GUTIERREZ HUAMPO

Uma banca de QUALIFICAÇÃO de DOUTORADO foi cadastrada pelo programa.
STUDENT : EULOGIO GUTIERREZ HUAMPO
DATE: 19/10/2023
LOCAL: Departamento de Eletrônica e Sistemas (sessão fechada ao público)
TITLE:

NUMERICAL ALGORITHMS FOR COMPUTING FRACTIONAL FOURIER TRANSFORMS: WITH APPLICATIONS TO CHIRP SIGNAL PROCESSING .

KEY WORDS:

Discrete Fourier transform, dyadicrationalapproximation, Fermat numbertransform, fractional Fourier transform, LFM signal. 

PAGES: 67
BIG AREA: Engenharias
AREA: Engenharia Elétrica
SUMMARY:

In thisthesisproject, lowcomplexityalgorithms for thecalculationofthefractional Fourier transform (FrFT) are introduced. Initially, state-of-the-artalgorithmswiththelowestarithmeticcomplexitiesavailable for calculatingthereferredtransform are investigatedanddescribed. Fromsuch a survey, a new algorithm for theapproximatediscrete Fourier transform (ADFT) isproposed; oneexplainshow it canbeusedtoreducethearithmeticcomplexityinvolved in thenumericalcalculationoftheFrFT. The Cooley-Tukeyalgorithmisgeneralizedusing a vectorizationoperatorsuitable for transformsofarbitrarylengths. The ADFT algorithmisbasedonreplacingtheso-calledtwiddlefactorswithdyadicrationales, which are more appropriate for hardware implementations. Thisstrategyallows, for example, to build a 64-point ADFT withoutmultipliers. Quantitativeresultsobtainedthroughouttheprojectdemonstratethattheaforementionedcomplexityreductioncanreach 68%, using a simplifiedmethod for calculatingthetransform. The effectivenessoftheproposedalgorithmisverifiedconsidering a single target directionofarrivalestimationapplication, in whichtheerrorusingthe ADFT-basedmethodreaches 0.8o, whenthenoiseofthechannelreaches -16 dB. In thisscenario, whenthealgorithmisappliedtopeaksearching in thefractional Fourier domain, it isdemonstratedhow it ispossibletoreducethesearchdimensionfrom 2D to 1D. In thecontinuityoftheresearch, oneintendstodevelopanaccelerator for computingtheFrFTbasedonchirpconvolutionusing Fermat numbertransforms (FNT), as outlined in a preliminaryway in thisproject. Anotherproblemthatcanbeaddressed later istheneedtorecalculatethediscreteFrFT in eachorseveral samples, something common in some real-time applications; in thesescenarios, thebasicalgorithms are notefficient.  

COMMITTEE MEMBERS:
Interno - 1882484 - JULIANO BANDEIRA LIMA
Interno - 1130403 - RICARDO MENEZES CAMPELLO DE SOUZA
Externo à Instituição - VITOR DE ANDRADE COUTINHO - UFRPE