本論文提出符合近似ANSI S1.11 class-2規格的18個頻帶濾波器組。所設計之濾波器組具有低群延遲、低運算複雜度、低匹配誤差等特色。相關發展技術可以分為以下幾項: 1) 先使用低通濾波器搭配離散餘弦轉換可以產生9個頻帶的等頻寬濾波器組，再將延遲單元(z-1)置換成全通濾波器，可產生9個頻帶之非等頻寬濾波器組; 2) 將離散餘弦轉換的輸入經過折疊減少其乘法運算量，再推導至遞迴離散餘弦轉換，以降低係數記錄量，最後使低通濾波器的頻譜可以拓展至想要的中心頻率; 3) 透過多速率架構來實現18個頻帶的近似ANSI S1.11 class-2規格(w =2)，與最新Liu et al.的文獻比較，本論文每個取樣點雖然增加16%加法，卻能降低66%的乘法，除此之外最大匹配誤差平均為3.05dB，明顯優於最新Wei et al.所提出的方法。由於本論文針對分析濾波器組進行硬體的實現，硬體設計上考量了不同的規格，未來可朝向可組態化發展。整體而言本論文提出的濾波器組設計，具有低群延遲與低運算量，在未來能實際應用在助聽輔具。

This thesis presents a novel algorithm and architecture design for 18-band quasi-class-2 ANSI S1.11 1/3 octave filterbank. The developing technique of this thesis is summarized as follows: 1) a simple low-pass filter (LPF) and discrete cosine transform modulation are utilized to generate a uniform 9-band filterbank first, and then we replace all elements of z-1 by all-pass filters (APF) to obtain the non-uniform filterbank; 2) a fast recursive structure and variable-length algorithm is further developed to efficiently accomplish DCT modulation. Then, the spectrum of LPF can be easily spanned and flexibly extended to the location of the desired central frequency; 3) an 18-band quasi-class-2 filterbank design is finally realized by combining with multi-rate concept and by following up the proposed design steps with parameter determinations. Compared with the latest Liu et al.’s quasi-class-2 ANSI S1.11 design, the proposed method totally has 72.3% reduction for multiplications per sample, 11.25-ms group delay, and 41 additions decreased per sample. The maximum matching error of the proposed method is averagely equal to 2.64 dB much smaller than that of the latest Wei et al.’s 3.75 dB. In implementation, the proposed design can be operated at 27.32 MHz which is easily to achieve 14.616 MHz real-time requirement. Overall, the proposed filterbank design would be a new solution for future applications in the area of hearing aids.

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