Integer DCTs and fast algorithms
A method is proposed to factor the type-II discrete cosine transform (DCT-II) into lifting steps and additions. After approximating the lifting matrices, we get a new type-II integer discrete cosine transform (IntDCT-II) that is float-point multiplication free. Based on the relationships among the various types of DCTs, we can generally factor any DCTs into lifting steps and additions and then get four types of integer DCTs, which need no float-point multiplications. By combining the polynomial transform and the one-dimensional (1-D) integer cosine transform, a two-dimensional (2-D) integer discrete cosine transform is proposed. The proposed transform needs only integer operations and shifts. Furthermore, it is nonseparable and requires a far fewer number of operations than that used by the corresponding row-column 2-D integer discrete cosine transform.