使用單一轉換函數的訊號表示法之改良

Improvement on Signal Representation Using Single Transformation

劉智偉(Chih-wei Liu)

指導教授 ： 張嘉銘

大同大學/電機資訊學院/資訊工程學系所/碩士(2008年)

摘要

以轉換函數為基礎之訊號表示法將訊號轉換至轉換函數域，使訊號的特徵更為明顯、表示上更有效率；盡可能用最少數量權重的基底函數來表示訊號，基於正交轉換方法使用單一正交函數有固定基底函數的限制，無法最佳的表示訊號，非正交轉換方法通常混合多個特性不同的轉換函數來表示訊號，然而，這種混合轉換法在計算量上是負擔。
顏先生對頻譜的研究後，提出了使用單一轉換函數搭配穆勒方法的演算法，可以找出更多更合適的基底以表示訊號，效率比混合轉換法佳，更勝單一轉換法，但是在用穆勒找最佳基底成份上花費過多的轉換運算。
在這篇論文中，提出了一個新的方法來改良顏先生的演算法，我們推導出類似SINC函數來趨近實際訊號頻譜中的成分，再將之抽取出作為轉換係數來表示訊號，在效率上與顏先生所提出的方法相當，在計算複雜度上也如預期地已被簡化。

關鍵字

正交轉換函數 ； 非正交轉換函數 ； 訊號表示法

並列摘要

Transform-based signal representation is the technique that transforming signal to transform domain to let the signal's features be more obvious and be represented efficiently. It use as minimum number of weighted basis functions as possible to represent signal. According to the orthogonal transform method employing single transform has the limitation of fixed basis functions. The non-orthogonal method mixed transforms to reach the goal. However, the mixed-transform method have burden on computational complexity.

Yan studied in the spectrum, and proposed an algorithm that using single transform applied Muller's method to find more dominant basis functions to represent signal. The performance is better than mixed-transform method, even than single transform method. But in order to compute the most dominant component by Muller's method takes much transform operations.

In this thesis, a new method to improve Yan's algorithm has proposed. We derive sinc-like function to fit into the spectrum of the practical signal and extract it as the transform coefficient to represent. The performance is nearly equal to Yan's algorithm and the complexity is simplified as our expectation.

並列關鍵字

signal representation ； orthogonal transform ； non-orthogonal transform

參考文獻

[1] J.-L. Yan, An adaptive algorithm for signal representation using one transform,"

in Department of Computer Science and Engineering, Tatung University, Jan

[3] A. P. Berg and W. B. Mikhael, Signal representation using adaptive parallel

[4] J. Ben-Arie and K. R. Rao, Nonorthogonal signal representation by gaussians

and Digital Signal Processing., volume 42, Jun. 1995, pp. 402{412.