New fast trigonometric transforms

New fast trigonometric transforms formed as combinations of discrete parametric Pontryagin transforms and discrete conjugate parametric Pontryagin transforms are introduced in this paper. They include as special cases such known orthogonal trigonometric transforms as the Fourier, Hartley, Wang, cosine and sine, Walsh, Chrestenson transforms, and many others. Different methods of efficient computation of the introduced transforms are described.