Adaptive Gaussian filtering and local frequency estimates using local curvature analysis

This paper presents an adaptive filtering technique for smoothing noisy sampled data. Due to the adaptive nature of the process, distortion of the information content is significantly reduced. Each point of the smoothed output is the result of a central convolution of the noisy data with a Gaussian. Gaussians of different width are used to produce each point of the smoothed output. The width of each Gaussian is selected, following local curvature estimates of the data, so that the smoothed points contain a nearly constant and acceptable error resulting from the smoothing process. Since each Gaussian has its half-power frequency equivalent, it is possible to infer the system of narrowest bandwidth that can be tolerated in transmitting the signal. The rationale used to determine the convolving Ganssians will be developed here along with brief discussions of applications.