Abstract:
The motivation for this invention evolved from a realization that a critical component was excluded from the information flow through a conventional digital filter, whether static or adaptive. Inputs can typically include the current input sample, previous samples, a priori knowledge Response and reference data. But the A/D sampler is not directly incorporated into the actual filter. Thus, standard filter design typically begins with a vector of uniformly sampled input data Fundamentally, non-uniform sampling of volatile signal can glean more information about a signal than uniform sampling at the Nyquist rate (if indeed that rate is known a-priori). Additional information might be gleaned from simultaneous pseudo-random non-uniform sampling, along with trend or volatility non-uniform sampling. In contrast to judicious non-uniform sampling, uniform sampling can be sub-optimal in extracting information per unit of effort expended. This filter design invention, named the D digital filter, extracts that additional information from non-uniform sampling to improve the effectiveness and performance of the filter's intended application. The performance measure or metric used depends on the application. For example, for standard noise filtering and signal smoothing applications, the D filter is designed to sharpen spectrum cutoff and to minimize ripples in the frequency spectrum, while preserving phase. Or, for adaptive applications, the D filter is designed to accurately or closely track changes from a reference condition, with fast response time. In all cases, the number of tap weights used is shown to be possibly significantly smaller than using conventional filter design techniques. This filter design relies on the D Scale architecture to perform the judicious non-uniform sampling. It also relies on D Scale based discrete decomposition equations for the continuous Fourier Transform, convolution and correlation functions, to guide the internal filter architecture. Further, it can accommodate the D Arithmetic to improve stability of adaptive filters, as well as add benefits to static filter operation. Finally, it introduces the D Signal to characterize linear as well as non-linear systems and communications channels. This digital filter design is comprised of up to seven (7) components. The components actually used in any implementation will depend on the application. Typically, adaptive filtering design will use many of the design components while static filters the fewest number. Various combinations of the D filter components are presented, to include static filters, adaptive filters and Kalman filters.