Efficient algorithms for the matrix cosine and sine

New Algorithms for Computing the Matrix Sine and Cosine Separately or Simultaneously

Several existing algorithms for computing the matrix cosine employ polynomial or rational approximations combined with scaling and use of a double angle formula. Their derivations are based on forward error bounds. We derive new algorithms for computing the matrix cosine, the matrix sine, and both simultaneously, that are backward stable in exact arithmetic and behave in a forward stable manner...

Discrete cosine and sine transforms - regular algorithms and pipeline architectures

In this paper, regular fast algorithms for discrete cosine transform (DCT) and discrete sine transform (DST) of types II–IV are proposed and mapped onto pipeline architectures. The algorithms are based on the factorization of transform matrices described earlier by Wang. The regular structures of the algorithms are advantageous when mapping them onto hardware although such algorithms do not rea...

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.