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.