Integer sinusoidal transforms based on lifting factorization

A general method is proposed to factor a discrete W transform (DWT) into lifting steps and additions. Then, based on the relationships among various types of discrete sinusoidal transforms, other types of transforms such as the discrete Fourier transform (DFT) and discrete cosine transform (DCT) are factored into lifting steps and additions. After approximating the lifting matrices, we get various types of new integer discrete transforms such as IntDWT, IntDFT and IntDCT which are floating-point multiplication free. Transforms which map integer to integer are also proposed. Fast algorithms are given for the new transforms and their computational complexities are analyzed. Based on a polynomial transform and an index mapping, multi-dimensional integer transforms are presented with especially low computational complexity.