Adaptive noise cancelling
The adaptive filter adjusts itself continuously and automatically to minimise the residual interference affecting the target signal at its output.
The power of the adaptive noise cancelling concept is that it requires no detailed a priori knowledge of the target signal or the interference.
The adaptive algorithm that optimises the filter relies only on ongoing sampling of the reference input and the noise canceller output.
The work was also published as a Stanford Electronics Labs report by Kaunitz and Widrow, Noise Cancelling Filter Study (1973).
[5] The initial proof of concept demonstrations of the noise cancelling concept (see below) for eliminating broadband interference were carried out by means of a prototype hybrid adaptive signal processor designed and built by Kaunitz and described in a Stanford Electronics Labs report General Purpose Hybrid Adaptive Signal Processor (1971).
[1][2][5] The power of the adaptive noise cancelling approach stems from the fact that the algorithm driving the iterative adjustment of weights in an adaptive filter is a simple, fully automatic iterative process that relies only on an ongoing sequence of sampling measurements of the noise canceller output and the reference r(t) = nr(t).
However, the physical characteristics of the adaptive filter must be generally suitable for producing an adjustable frequency response or transfer function that will transform the reference signal nr(t) into a close estimate of the corrupting interference, ñp(t), through the iterative adjustment of the filter weights.
[1][5] A 1975 paper published in the Proceedings of the IEEE by Widrow et al., Adaptive Noise Cancelling: Principles and Applications[2], is now the generally referenced introductory publication in the field.
This paper sets out the basic concepts of adaptive noise cancelling and summarises subsequent early work and applications.
The above expression shows ξ to be a quadratic function of the weight vector W, a multi-dimensional paraboloid with a single minimum that can be reached from any point by descending along the gradient.
In the case of the usual digital tapped delay line filter, the vector Xk is simply the last set of samples of the filter input x(t) and the LMS algorithm results in: Wk+1 = Wk - μekXk where k represents the kth step in the iteration process, μ is the adaptation constant that controls the rate and stability of the adaptation process and ek and Xk are samples of the error and the input vector respectively At the completion of the training phase, the adaptive filter has been optimised to produce the desired optimal transfer function.
So the adaptive filtering of the reference actually strives to suppress the overall signal power at the noise canceller output.
So, in aiming to minimise the error, using a reference as input, which is related only to the interference, the best the adaptive filter can do, in generating an optimal estimate of the primary input, the desired response, is to generate the optimal estimate of the interference at the primary sensor ñp(t).
This will result in minimising the overall effect of the interference at the noise canceller output whilst leaving the target signal s(t) unchanged.
An analysis of noise cancelling where s(t) and n(t) are assumed to be bounded deterministic signals was presented by Kaunitz[1] in his PhD dissertation, where time averaging is used.
This linear combiner[3] interfaced to a small HP 2116B digital computer that ran a version of the LMS algorithm.
[7] The experimental arrangement used by Kaunitz in the photo below shows the loudspeaker emitting the interference, the two microphones used to provide the primary and reference signals, the equipment rack, containing the hybrid adaptive filter and the digital interface, and the HP 2116B minicomputer on the right of the picture.
Data was provided by Drs Eugene Dong and Walter B Cannon in the form of a multi-track magnetic tape recording[1][5] of electrocardiograms.
[1][3]Adaptive noise cancelling techniques have found use in a wide range of situations, including the following: In these situations, a suitable reference signal can be readily obtained by placing a sensor near the source of the interference or by other means (e.g. a version of the interfering ECG free from the target signal).
As explained above, adaptive noise cancelling is a technique used in communication and control to reduce the effect of additive interference corrupting an electric or electromagnetic target signal.
