Reducing Gaussian Noise Using Distributed Approximating Functionals

The denoising characteristics for the representation of experimental data in terms of the Hermite Distributed Approximating Functionals (HDAF's) are analyzed with respect to signals corrupted with Gaussian noise. The HDAF performance is compared to both the ideal window and running averages representations of the same data. We find that the HDAF filter combines the best features of both. That is, the HDAF filter provides approximately the same noise reduction and bandwidth as the ideal filter while at the same time remaining limited in range in both the physical and Fourier spaces.