Filters which are used to pass a signal corrupted by noise may be of two types: fixed filters or adaptive filters.  For the proper design of fixed filters, the properties of the signal and the noise must be known.  However, adaptive filters are able to adjust their weighted taps automatically, the design requiring no prior knowledge of either the signal or noise characteristics. 
Filters utilizing noise cancellation, that is, adaptive filters, utilize an auxilliary or reference input derived from one or more sensors located in an environment where the signal is very weak.  This reference input is filtered and sent to a different signal circuit where it is subtracted from the primary input which contains both signal and some common noise, thereby cancelling some of the primary noise. 
The basic concept of adaptive noise cancelling is illustrated in FIG.  2.  A signal s is received by a sensor that also receives a noise n.sub.0 which has no correlation with the desired signal s. The combination of the signal s and noise n.sub.0 comprise the primary input to the adaptive noise canceller.  Another sensor, removed from the first sensor, receives a noise signal n.sub.1 which is uncorrelated with the signal but is correlated with the noise signal n.sub.0, the second sensor providing the reference input to the canceller.  The noise n.sub.1, after filtering, produces an output r(k) which is as similar as possible to n.sub.0.  As is shown in FIG.  2, the filter ouput r is subtracted from the primary input signal, s+n.sub.0, in a differencing circuit, to generate the output of the canceller, .epsilon.=s+n.sub.0 -r. 
An adaptive filter, such as the adaptive noise canceller shown in FIG.  2, is different from an ordinary fixed filter in that it automatically adjusts its own impulse response.  The adjustment is done through an algorithm, the Widrow-Hoff algorithm in this invention, which is a function of the error signal .epsilon.,  the error signal being dependent on the current output of the filter.  If the correct algorithm parameters (i.e., time constant and update rate), are chosen, the noise canceller operates under changing conditions to adjust itself constantly, thereby maintaining minimum power in the error signal. 
In noise cancelling system of the type described herein it has been determined that a practical objective is to produce an output signal z=s+n.sub.0 -v that is a best fit to the signal s from the standpoint of least means aquare (LMS) error power.  This objective is accomplished by feeding a portion 2.mu.e of the system output signal r(i) back to the adaptive filter and adjusting the filter tap weights through an LMS adaptive algorithm to minimize total system output power.  From this, it may be seen that in an adaptive noise cancelling system, the system output signal, or a portion of it, serves as the error signal for the adaptive process. 
The background information in this section has been adapted from the article entitled "Adaptive Noise Cancelling: Principles and Applications," by Widrow, Bernard, et al.,  which appeared in the Proceedings of the IEEE, Volume 63, No.  12, December 1975.