A Tutorial of Integer Transform

The integer transform (such as the Walsh transform, the Haar transform) is a discrete transform that all the entries in the transform matrix are integers. For software and hardware, the integer transform is much easier to be implemented because there is no real number multiplication, but performance is not guaranteed. By contrast, the non-integer transform (such as the DCT, the DFT) has higher performance, but the real number multiplication is needed. As we know, more computation time and implementing cost are required when there are more real number multiplications, and, therefore, this is the purpose why the integer transform has been researched. In this tutorial, I survey the development of integer transform since old days. The first time integer transform was mentioned is about the color space transform, and then the DCT approximation by prototype matrices was proposed. For example, (1.1) is the SIM transform whose entries are summation of 2 k , and so is its inverse transform shown in (1.2).