ON GENERALIZED SINE AND COSINE FUNCTIONS

Integral Transforms of Fourier Cosine and Sine Generalized Convolution Type

Discrete Cosine and Sine Transforms Generalized to Honeycomb Lattice

The discrete cosine and sine transforms are generalized to a triangular fragment of the honeycomb lattice. The two-variable orbit functions of the Weyl group A2, discretized simultaneously on the weight and root lattices, induce the family of the extended Weyl orbit functions. The periodicity and von Neumann and Dirichlet boundary properties of the extended Weyl orbit functions are detailed. Th...

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.