Integer DCTs and fast algorithms

A method is proposed to factor the type-II discrete cosine transform (DCT-I I) into lifting steps and additions. After approximating the lifting matric es, we get a new type-II integer discrete cosine transform (IntDCT-II) that is float-point multiplication free. Based on the relationships among the v arious types of DCTs, we can generally factor any DCTs into lifting steps a nd additions and then get four types of integer DCTs, which need no float-p oint multiplications. By combining the polynomial transform and the one-dim ensional (1-D) integer cosine transform, a two-dimensional (2-D) integer di screte cosine transform is proposed. The proposed transform needs only inte ger operations and shifts. Furthermore, it is nonseparable and requires a f ar fewer number of operations than that used by the corresponding row-colum n 2-D integer discrete cosine transform.