HSM(High Speed Machining)is a revolutional technology development following NC technology in 20 century. Its basic prosperities are high cutting speed(5～10 times faster than normal cutting speed),fast feeding(40～180 m/min) and great acceleration(1～2 g).
A class of fast orthogonal transformations for finite strings of data are described.
We derive a fast algorithm to compute the coefficients.
This article genralizes the fast Fourier transform algorithm to the computation of Fourier transforms on compact Lie groups.
These results may all be viewed as generalizations of the fast Fourier transform algorithms on the circle, and of recent results about Fourier transforms on finite groups.
Spherical harmonic series have many of the same wonderful properties as Fourier series, but have lacked one important thing: a numerically stable fast transform analogous to the Fast Fourier Transform (FFT).