Praćenje trenutne frekvencije signala primjenom Hilbertove transformacije

undergraduate thesis

• Title (english): Instantaneous frequency estimation using the Hilbert transform
• Author: Filip Cimermančić
• Mentor: Vedran Bilas (mentor)
• Committee member: Vedran Bilas (predsjednik povjerenstva)
• Committee member: Darko Vasić (član povjerenstva)
• Committee member: Dinko Oletić (član povjerenstva)
• Granter: University of Zagreb; Faculty of Electrical Engineering and Computing; Zagreb
• Defense date and country: 2017-07-10, Croatia
• Scientific / art field, discipline and subdiscipline: TECHNICAL SCIENCES; Computing
• Scientific / art field, discipline and subdiscipline: TECHNICAL SCIENCES; Electrical Engineering

Abstract

Hilbertova transformacija je operator koji omogućuje jednostavno dobivanje amplitude i faze ulaznog signala koristeći analitički signal. Analitički signal je zapis u kojem je realna komponenta ulazni signal, a imaginarna komponenta Hilbertova transformacija signala. Koristeći testne signale i programski alat Matlab, u prvom eksperimentu se pokazalo kako pomoću analitičkog signala možemo pratiti trenutnu frekvenciju ulaznog signala, te su rezultati eksperimenta popraćeni grafičkim prikazom izlaznih signala. U drugom eksperimentu algoritam za izračunavanje analitičkog signala implementiran je na ARM Cortex M3 procesor. Implementirani algoritam radi na principu računanja Brze Fourierove transformacije, izjednačavanja dijela spektra koji odgovara negativnim frekvencijama s nulom i računanja Inverzne brze Fourierove transformacije takvog spektra. U procesoru se računa i faza signala, a izlazni signal je frekvencija ulaznog signala koja se učita i crta u Matlabu. Gledajući dobivene rezultate i uspoređujući ih s onima iz Matlaba, može se vidjeti kako algoritam za ARM procesor estimira trenutnu frekvenciju signala, što dokazuje da je algoritam uspješno implementiran.

Abstract (english)

Hilbert transform is an operator that allows simple calculation of the amplitude and phase of the input signal using the analytic signal. Analytic signal is a signal whose real part is the input signal and its imaginary part is Hilbert transform of the input signal. Using programming tool Matlab in first experiment, it was shown how the frequency of the input signal can be monitored using the analytic signal. The results were displayed as graphs that represent frequency of the input signal. In second experiment, the algorithm for calculating the analytic signal was implemented on ARM Cortex M3 processor. Implemented algorithm calculates Fast Fourier transform of the input signal, replaces coefficients that correspond to negative frequencies with zeros, and calculates Inverse fast Fourier transform. Algorithm calculates phase of the signal and the output signal from the processor is signal frequency which is imported into Matlab and drawn. Looking at the results of the experiment and comparing them with the results calculated in Matlab, it’s apparent that ARM algorithm estimates instantaneous signal frequency, which proves that the algorithm is successfully implemented.

• Keywords: Hilbertova transformacija; analitički signal; frekvencija; ARM; eksperiment
• Keywords (english): Hilbert transform; analytic signal; frequency; ARM; experiment
• Language: croatian
• URN:NBN: urn:nbn:hr:168:435567
• Study programme: Title: Electrical Engineering and Information Technology; Study programme type: university; Study level: undergraduate; Academic / professional title: sveučilišni/a prvostupnik/ prvostupnica (baccalaureus/baccalaurea) inženjer/inženjerka elektrotehnike i informacijske tehnologije (sveučilišni/a prvostupnik/ prvostupnica (baccalaureus/baccalaurea) inženjer/inženjerka elektrotehnike i informacijske tehnologije)
• Type of resource: Text
• File origin: Born digital
• Access conditions: Closed access
• Created on: 2019-03-13 19:35:31