Abstract: Based on the unified form of the discrete trigonometrical transform,under orthogonality  conditions，a kind of fast algorithms with halved structure is proposed,the parallel times being ｏ（Ｎｌｏｇ2 Ｎ).So the fast algorithms of discrete sine transform,the discrete cosine transform and the discrete W transform ar
e unified.

Key words: trigonometrical transform, orthogonality transform, fast algorithm