  The wavelet analysis technique is a powerful tool and is widely used in broad
disciplines of engineering, technology, and sciences. In this work, we present
a novel scheme of constructing continuous wavelet functions, in which the
wavelet functions are obtained by taking the first derivative of smoothing
functions with respect to the scale parameter. Due to this wavelet constructing
scheme, the inverse transforms are only one-dimensional integrations with
respect to the scale parameter, and hence the continuous wavelet transforms
constructed in this way are more ready to use than the usual scheme. We then
apply the Gaussian-derived wavelet constructed by our scheme to computations of
the density power spectrum for dark matter, the velocity power spectrum and the
kinetic energy spectrum for baryonic fluid. These computations exhibit the
convenience and strength of the continuous wavelet transforms. The transforms
are very easy to perform, and we believe that the simplicity of our wavelet
scheme will make continuous wavelet transforms very useful in practice.
