Application of Q-measure Techniques to Adaptive Nonlinear Digital Filtering

A highly adaptive nonlinear digital filtering technique called the Q-Filter is described. The Q-Filter is defined as a Choquet integral with respect to a Q-Measure over a finite window of observations. In addition to robustness, the advantage of the Q-Filter is that it can behave as a combination of different filters, so that a single Q-Filter can be used instead of applying an expensive sequence of conventional filtering operations. In this paper we present the Q-Filter in application to a real-valued signal processing task, with a regression algorithm, so that the parameters of the filter can be tuned automatically. This algorithm also resolves the signal scaling and shifting issues associated with the direct filtering operation. The Q-Filter model is tested on acoustic heartbeat sound data. The experiments show that the proposed model can be used to map input signals to their corresponding target signals through learning.