The Fourier series method is a basic theory for function transformation, while there are Gibbs effects for such types treatments with finite number of terms. Many mathematicians have contributed the intelligence for this field, such as Hardy [1] and Chen [2], and so on. In this paper, The combined waves theory was proposed, in which the Fourier series have been discussed by Taylor series whose first order function terms shows Gibbs effect naturally, the Gibbs effect may the principle of the word underlying logic, Some basic phenomena had discussed and explained.