In this paper, a new filtering method is presented for simultaneous noise
reduction and enhancement of signals using a fractal scalar conservation law
which is simply the forward heat equation modified by a fractional
anti-diffusive term of lower order. This kind of equation has been first
introduced by physicists to describe morphodynamics of sand dunes. To evaluate
the performance of this new filter, we perform a number of numerical tests on
various signals. Numerical simulations are based on finite difference schemes
or Fast and Fourier Transform. We used two well-known measuring metrics in
signal processing for the comparison. The results indicate that the proposed
method outperforms the well-known Savitzky-Golay filter in signal denoising.
Interesting multi-scale properties w.r.t. signal frequencies are exhibited
allowing to control both denoising and contrast enhancement