多波元轉換應用於聲學迴音消除

Abstract

本論文主題為多波元轉換應用於聲學迴音消除之研究。近年來， Geronimo、Hardin和Massopust結合碎形內插函數的理論和多解析度分析 的概念，建構出兩組以上具有對稱性的比例函數與波元函數，並求得相對 應的係數矩陣。本文首先提出一個二元樹架構的多波元小包轉換，之後連 結適應性濾波器，並應用於迴音消除的問題上。基於多波元小包轉換之分 解，我們將推導出可完全消除迴音的條件，為了符合此最佳條件，我們更 進一步提出一個修正型架構之多波元小包轉換。對兩種不同的架構，將有 一些實驗作比較，實驗結果顯示修正型架構之多波元小包轉換的效果優於 二元樹架構的多波元小包轉換。根據之前所分析出的迴音消除最佳條件， 我們將提出一測定法，來判斷係數矩陣滿足最佳條件的程度。基於該測定 法的使用，我們提出一套程序，在所有對應於非對稱性比例函數和波元函 數的係數矩陣中，找出一組最佳的係數矩陣。針對兩種不同架構，選出不 同的最佳係數矩陣，實際應用於迴音消除的問題上。在實驗的比較中，使 用修正型架構之多波元小包轉換配合相對的最佳係數矩陣，將會有最好的 結果。 This paper investigates a new technique using discrete multiwavelet transformsin acoustic echo cancellation. Recently, Geronimo, Hardin, and Massopust constructed two symmetric scaling functions, two associated wavelets and corresponding coefficient matricesfrom the theories of fractal interpolation functions and the notion of multiresolution analysis. In this paper, we introduce a binary tree-structured multiwavelet packetcoupled with adaptive filtering and apply it to acoustic echo cancellation. Based on the multiwavelet packet decomposition, we derive the condition of complete echo cancellation. To approach this optimal condition,we propose a structure-modified multiwavelet packet.Our experiments show that the structure-modified multiwavelet packetoutperforms the binary tree-structured one,with both using symmetric scaling functions. We next derive a measure to check how wellthe optimal condition is satisfied.Based on this measure,We propose a procedure to find the optimal coefficient matriceswith asymmetric scaling functions and associated wavelets in the echo cancellation problem.We obtain different optimal coefficient matrices forthe multiwavelet packets with different structures.The experiment results on echo cancellationusing the optimal coefficient matrices are presented.Comparisons to other schemesshow that the structure-modified multiwavelet packetwith optimal coefficient matrices has the best performance.