Sine and cosine types of generating functions

Discrete Cosine and Sine Transforms

Local Sine and Cosine Bases

19 and = 1 + 1 m ; m a positive integer. If we let w(x) 1 p 2 R 1 ?1 e ixx ()dd, then w is a \mother function" that generates a wavelet basis (giving us a Multi Resolution Analysis) m ; m a positive integer. x6. Concluding remarks. We repeat that the local bases we developed in x2. were introduced by Coifman and Meyer, and their use in obtaining the smooth wavelet bases were pointed out to us b...

Fractional Cosine and Sine Transforms

The fractional cosine and sine transforms – closely related to the fractional Fourier transform, which is now actively used in optics and signal processing – are introduced and their main properties and possible applications are discussed.

On composition of generating functions

In this work we study numbers and polynomials generated by two type of composition of generating functions and get their explicit formulae. Furthermore we state an improvementof the composita formulae's given in [6] and [3], using the new composita formula's we construct a variety of combinatorics identities. This study go alone to dene new family of generalized Bernoulli polynomials which incl...

Fast Computing of Discrete Cosine and Sine Transforms of Types VI and VII

The Discrete Sine and Cosine Transforms (DST and DCT) have already received considerable attention due to their use in source coding. The DCT of type-II (DCT-II) is at the core of standards for image and video compression, such as JPEG, H.26x-series, and MPEG 1-4 standards. The DST of type-I was suggested as a basis for Recursive Block Coding technique. The DCT and DST of type IV are used in de...