傅立葉與希爾伯特轉換在訊號處理上之探究

Abstract

本文的主要目的，是將訊號處理中所使用到的方法，尤其是傅立葉及希爾伯特轉換進行整合，探究其數學原理、完備其數學理論的證明以及在訊號處理上的應用，並介紹希爾伯特-黃轉換。而於最後進行各個轉換方法的優缺點比較並分析其所適用的信號特性。

The main purpose of this thesis is to investigate the mathematical background and complete the proof of theorems of methods used in signal processing, especially Fourier and Hilbert transform and introduce Hilbert-Huang transform. Finally we compare the advantages and shortage of each transform and discuss the suitable situations for each method.