對於數位訊號的處理，離散凌波轉換提供了完整的理論與方法。但是在電腦實做的時候，離散凌波轉換換有一點小小的缺點，所以在 [1] 中提出了週期化的方法，然而，我們也利用一點小技巧，找到了一個新的演算法── nilup 來做影像放大。同時，在一維訊號合成的實驗中，我們發覺離散凌波轉換竟然會有類似超射現象發生，這是我們所不願見的，但是實驗了幾種方法後卻還是避免不，這個問題有待我們解決。
同時，我們都知道凌波轉換對於 point singularities 的表現是無庸置疑的，甚至計算量都略勝於快速凌波轉換，但是 point singularities 只是眾多ingularities 的冰山一角，而且明顯的，凌波轉換在二維影像的邊上
確實表現不佳。對於這個問題 Donoho 提出了直脊函數的想法，以針砭凌波轉換之不足。所以第二章裡我們取經於 Donoho ，以解決我們的第二個問題。

For the discrete wavelet transform, we find a new algorithm, named nilup, to reconstruction the digital signal. But when we experiment with 1-D digital signal, there is an affinity with Gibbs phnomenon. If we wnat to do 2-D experiment, this is the problem we should solve first.
We know that wavelets analysis has ability to effciently represent functions which are smooth away from point singularities. But point sinlarities are just one possible type of singularity, wavelets
do not yield coefficients as they did point singularities. To this problem, Donoho construct a new orthonormal basis, say ridgelets. In this article, we will introduce the readers to ridgelets.

1 單維彰，凌波初步，全華科技圖書公司，1999。
2 David L. Donoho , Orthonormal Ridgelets and Linear Singularities,
Technical Report, Statistic, Stanford, 1998. To appear in SIAM J. Math. Anal.
3 Emmanuel J. Candes and David L. Donoho, SIAM, Philadelphia,1992.
4 Ingrid Dauvachies, Ten lectures on Wavelets, SIAM,1992.
5 Stephane Mallat, a Wavelet Tour on WAvelets,Second ed., Academic Press, 1999.
6 C.K Chui An Introdection to Wavelets Academic Press, New York, 1992.
7 I-Liang Chern, Chien-Chang Yen, Interpolating Wavelets and Difference Waveletas,March 11,1998.