利用適應性重建濾波器組之多速率訊號處理

Abstract

傳統的重建濾波器組被設計成滿足完整重建的特性。大部份的設計假設分 頻訊號沒有失真，但是在實際的應用上，這個假設常常不合理。例如，分 頻訊號由於量化而有外加雜訊造成失真、由於傳輸而有通道造成失真、由 於訊號處理而有濾波器造成失真。在這些情形下，傳統的設計不能得到滿 意的結果。在本論文中，我們使用適應性重建濾波器組來應付這個問題。 特別地，我們考慮遞迴式最小平方 (RLS) 演算法，因為它收斂快且所導 致的誤差小。一個關於 RLS 演算法的問題是，它需要大量的計算。雖然 能有效減少計算的快速 RLS 演算法已有發展，由於在合成過程中的補點 運算，使得他們在這□並不適用。利用多項拆解法，我們提出一個新的演 算法能夠把分頻重建變成一個多通道濾波的問題。使用這種做法，我們可 以應用多通道快速 RLS 演算法，並且有效降低計算複雜度。這個想法也 被延伸到 IIR 重建濾波器組上面。對 IIR 重建濾波器組，這個問題變得 更複雜。因為 IIR 濾波器的回授部份與正向部份並沒有相同的多相拆解 結構，因此我們提出了一個新的分頻結構以取代回授部份來克服這個問題 。以上所提的適應性重建濾波器組可用於傳輸多工器系統與聲訊迴音消除 上。另外一種做法是使用多速率卡曼濾波器來執行重建，我們探討了這種 作法的應用。首先考慮的是多速率卡曼等化器，當通道具有頻譜零點時， 可以發現多速率卡曼濾波器優於傳統的卡曼等化器。其次我們考慮了在高 階自相關彩色雜訊下閃躲目標追蹤的問題。在這個應用上，量測訊號先被 拆解為分頻訊號，每個分頻的彩色雜訊便以一階的自關程序來模擬。並且 ，我們也提出了一個新的去量測訊號相關的方法，使目標的運動得以估計 。這方法的優點是彩色雜訊的相關訊息不需事先知道，而所有的處理能用 於即時的運作。使用這個方法，追蹤性能已有大大的提升。 The conventional reconstruction filter banks are designedto satisfy the perfect reconstruction property. Most designs assumethat subband signals are free of distortions. However, in practicalapplications, this assumption is often not valid. For example,subband signals may be distorted by additive noise due to quantization,by channel due to transmission, or by filters due to signal processing.In such cases, conventional designs cannot yield satisfactory results.In this thesis, we use adaptive reconstruction filter banks todeal with the problem. Specifically, we consider therecursive least squares (RLS) algorithm since it converges fast andthe reconstruction error is small. One problem associated with the RLS algorithmis that it requires extensive computations. Although fast RLS algorithms, which can substantially reduce computations, have been developed, they are not suitable here due to the interpolation operations involvedin the synthesis process. By polyphasedecomposition, we propose a new algorithm that can formulate the subbandreconstruction as a multichannel filtering problem. Using this formulation,we can apply multichannel fast RLS algorithms and substantially reduce computational complexity. This idea is then extended to IIR reconstructionfilter banks. In IIR filter banks, the problem becomes more involvedsince the feedback part of the IIR filter and the feedforward part cannotapply the same polyphase decomposition structure. Thus, we propose a new subbandstructure to replace the feedback part for overcoming the problem. The proposed adaptive reconstructionfilter bank is then applied to transmultiplexer systems and acoustic echo cancellation.There is another approach, which uses the multirate Kalman filter, performing the reconstruction. We explore the applicationsof this approach. We first consider the multirate Kalman equalization.It is shown that the multirate Kalman equalization can outperform theconventional Kalman equalization when the channel possesses spectralnulls. We then consider the problem of maneuvering target tracking with high-order autoregressive (AR) colored noise. In this application, the measurement signal is firstdecomposed into subbands. The colored noise in each subband is thenmodeled by a first-order AR process. A new measurementdecorrelation method is proposed such that the target motion can beestimated. The advantage of this approach isthat no $a$ $priori$ knowledge of the colored noise is required. Allthe processing can be carried out in the real-time fashion. Usingthis approach, the tracking performance can be greatly enhanced.