  The power spectrum estimator based on the discrete wavelet transform (DWT)
for 3-dimensional samples has been studied. The DWT estimator for
multi-dimensional samples provides two types of spectra with respect to
diagonal and off-diagonal modes, which are very flexible to deal with
configuration-related problems in the power spectrum detection. With simulation
samples and mock catalogues of the Las Campanas redshift survey (LCRS), we show
(1) the slice-like geometry of the LCRS doesn't affect the off-diagonal power
spectrum with ``slice-like'' mode; (2) the Poisson sampling with the LCRS
selection function doesn't cause more than 1-$\sigma$ error in the DWT power
spectrum; and (3) the powers of peculiar velocity fluctuations, which cause the
redshift distortion, are approximately scale-independent. These results insure
that the uncertainties of the power spectrum measurement are under control. The
scatter of the DWT power spectra of the six strips of the LCRS survey is found
to be rather small. It is less than 1-$\sigma$ of the cosmic variance of mock
samples in the wavenumber range $0.1 < k < 2$ h Mpc$^{-1}$. To fit the detected
LCRS diagonal DWT power spectrum with CDM models, we find that the best-fitting
redshift distortion parameter $\beta$ is about the same as that obtained from
the Fourier power spectrum. The velocity dispersions $\sigma_v$ for SCDM and
$\Lambda$CDM models are also consistent with other $\sigma_v$ detections with
the LCRS. A systematic difference between the best-fitting parameters of
diagonal and off-diagonal power spectra has been significantly measured. This
indicates that the off-diagonal power spectra are capable of providing
information about the power spectrum of galaxy velocity field.
