  A class of high-order lowpass filters, the discrete singular convolution
(DSC) filters, is utilized to facilitate the Fourier pseudospectral method for
the solution of hyperbolic conservation law systems. The DSC filters are
implemented directly in the Fourier domain (i.e., windowed Fourier
pseudospectral method), while a physical domain algorithm is also given to
enable the treatment of some special boundary conditions. By adjusting the
effective wavenumber region of the DSC filter, the Gibbs oscillations can be
removed effectively while the high resolution feature of the spectral method
can be retained. The utility and effectiveness of the present approach is
validated by extensive numerical experiments.
