Malozemov, Vassili N.; Masharsky, Sergey M.

COMPARATIVE STUDY OF TWO WAVELET BASES (in Russian)

malv@gamma.math.spbu.ru

   Two elementary wavelet bases producing discrete Haar
transforms   $H_f$ and $H_g$ are considered. The first transform
$H_f$ is related   with subsampling in frequency, the second one
$H_g$ is related with   subsampling in time. The necessary
information on described bases (recurrent relations, explicit
expressions, decomposition formulae) is given.   Wavelet
expansions of unit impulse shifts are written. Analogues of   a
sampling theorem for considered wavelet bases are obtained.
The concept of a logarithmically autoreversal spectrum is
introduced. The relation between signals $x$ and $y$ having
$H_f(y)=H_g(x)=:X$, provided that the spectrum $X$ is
logarithmically   autoreversal, is established. The d imension of
a set of   logarithmically autoreversal spectra is calculated.

Subj. Class.:   42C10, Fourier series in special orthogonal functions

Comment: PostScript, 14 pp., 2 pictures, 1 table.