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Monday, October 3, 2011

The Adaptive Noise Canceller as a High-Pass Filter

In 1975 Widrow et. al. introduced a scientific paper about Adaptive Noise Cancellers (ANCs). Since then, ANCs have been used extensively in different applications. This article is about the use of an ANC as a simple, yet powerful, high-pass filter.

As shown in the figure, a reference DC signal x(n)=1 is fed to a single-coefficient ANC. The noise estimate y(n) is the multiplication of the DC signal x(n) times the single coefficient, or weight, w(n). The noise estimate is then subtracted from the input signal d(n) to obtain a noise-free sample e(n) which can be considered the output of the ANC. e(n) is also fed back into the Least Mean Squares (LMS) Algorithm block, which calculates a new value for the weight w(n+1) based on the correlation between the reference signal x(n) and the error signal e(n) using the equation
w(n+1) = w(n) + mu * e(n) * x(n)
where mu is the adaptation step, usually a very small factor in the order of 0.01.

Widrow et. al. proved in their 1975 paper that this structure is equivalent to a high-pass filter with a corner frequency determined by mu.

The ANC is indeed a very simple, yet powerful, structure that has many applications in different disciplines. Recently, I've used the ANC as proposed by Widrow et. al. with some modifications for adaptive cancellation of power-line interference signals from the electrocardiogram (ECG), as shown in this paper.