Power Electronic Systems

2 An Alternative Class of Orthogonal Functions

Orthogonal properties [1] of the familiar sine–cosine functions have been known to the academic community for more than two centuries. But using such functions in an elegant manner to solve complex analytical problems was initiated by the work of the famous mathematician Baron Jean Baptiste Joseph Fourier [2]. With the passage of time, Fourier analysis established itself as one of the major analytical techniques.

In many areas of electrical engineering, the basis for any analysis is a system of sine–cosine functions. This is mainly due to the desirable properties of frequency domain representation of a large class of functions encountered in theoretical and practical aspects of engineering design. ...