Trainable nonlinear filters

Abstract

In conventional filter design there are generally two underlying assumptions. First, it is assumed that the precise nature of the operation to be performed on a signal is known. Second, the signal conditioning is generally a linear operation. (There are certain notable exceptions such as waveform hard-limiting in FM demodulation; but even in this example, it is the zero-crossing timing which is of interest -- no information is being extracted from the signal in the limiting process. ) If the nature of the transfer function is known and linear, there are many straight-forward approaches to designing appropriate filters. However, in certain interesting classes of signal processing applications, the description of the desired filter may not be known, or if it is known, it may be nonlinear and exhibit instability when implemented directly. If there are empirical data which represent the class of signals to be operated on in such cases, adaptive learning network (ALN) procedures may be used to synthesize filter forms which estimate or predict the desired parameter. The filters are transversal and are therefore always stable. Questions of stability associated with recursive filters are avoided. This paper presents a procedure for using ALN training techniques to synthesize a nonlinear filter directly from empirical data. The example used involves estimating the energy within a specified band of a broad-band signal. Though the design of a conventional energy estimator is straight forward, this knowledge was not used in the ALN training process -- an important consideration. An after-the-fact comparison is made between the ALN and a conventional system using an eight-pole Butterworth band pass filter.