[Authors]
 V. N. Malozemov, S. M. Masharsky

[Title]
 Glassman formula, fast Fourier transform and wavelet expansions

[AMS Subj-class]
 65T50 Discrete and fast Fourier transforms 
 65T60 Wavelets 

[Abstract]
 Using Glassman formula and the permutation called reverse, three
 variants of factorization of Fourier matrix of order $N=n^s$
 are obtained. Basing on these factorizations, three recurrent
 sequences of orthogonal bases having a block structure are
 constructed in a space of discrete periodic signals.
 Generalized wavelet bases are formed from blocks which belong
 to different bases of a recurrent sequence. Fast algorithms
 for computing the expansion coefficients for all described bases
 are offered.

[Keywords]
 fast Fourier transform, discrete periodic signals, wavelet expansions

[Comments]
 33 pp., Russian

[Contact e-mail]
 malv@gamma.math.spbu.ru
 smash@scientist.com