The Harr Transform:Its Theory and Computer Implementation.

摘要

Haar functions, square wave step functions of various rates of value change or 'sequency', take on the values +1, -1, and 0 in the interval (0, 1). Since Haar functions form an orthogonal system, any digital function or set of digital data can be represented as a linear combination of these functions, just as Fourier analysis represents data as a linear combination of sines and cosines. The Fast Haar Transform algorithm developed in this paper drastically reduces the number of operations required to transform a set of 16 data elements, i.e., from 256 to only 30. Therefore, one of the chief advantages that the Fast Haar Transform has over the Fast Fourier Transform is that it is between four and five times faster in terms of the number of computer calculations required, thereby reducing the cost of the computer time needed by 80 percent.