[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