High accurate sine and cosine interpolation with repeated differentiation ability obtained by fast expansions technique

A Floating-Point Processor for Fast and Accurate Sine/Cosine Evaluation

A VLSI architecture for fast and accurate floating-point sine/cosine evaluation is presented, combining floating-point and simple fixed-point arithmetic. The algorithm implemented by the architecture is based on second-order polynomial interpolation within an approximation interval which is partitioned into regions of unequal length. The exploitation of certain properties of the trigonometric f...

Fast Hankel transform by fast sine and cosine transforms: the Mellin connection

The Hankel transform of a function by means of a direct Mellin approach requires sampling on an exponential grid, which has the disadvantage of coarsely undersampling the tail of the function. A novel modified Hankel transform procedure, not requiring exponential sampling, is presented. The algorithm proceeds via a three-step Mellin approach to yield a decomposition of the Hankel transform into...

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.