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  • This module is included inLens: richb's DSP resources
    By: Richard BaraniukAs a part of collection:"Adaptive Filters"

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    "A good introduction in adaptive filters, a major DSP application."

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Adaptive Interference (Noise) Cancellation

Module by: Douglas L. Jones

Summary: Adaptive interference (or noise) cancellers are widely used. An adaptive noise canceller adaptively filters a noise reference input to maximally match and subtract out noise or interference from the primary (signal plus noise) input.

Goal: Automatically eliminate unwanted interference in a signal.
fig1AdaptiveInter.png
Figure 1
The object is to subtract out as much of the noise as possible.
Example 1: Engine noise cancellation in automobiles 
fig2AdaptiveInter.png
Figure 2
The firewall attenuates and filters the noise reaching the listener's ear, so it is not the same as n k ' n k ' . There is also a delay due to acoustic propagation in the air. For maximal cancellation, an adaptive filter is thus needed to make n k ' n k ' as similar as possible to the delayed n k n k .
fig3AdaptiveInter.png
Figure 3
Problem 1
What conditions must we impose upon the microphone locations for this to work? (Think causality and physics!)

Analysis of the interference cancellor

fig4AdaptiveInter.png
Figure 4
E ε k 2=E s k + n k - y k 2=E s k 2+2E s k n k - y k +E n k - y k 2 ε k 2 s k n k y k 2 s k 2 2 s k n k y k n k y k 2 We assume s k s k , n k n k , and n k ' n k ' are zero-mean signals, and that s k s k is independent of n k n k and n k ' n k ' . Then E s k n k - y k =E s k E n k - y k =0 s k n k y k s k n k y k 0 E ε k 2=E s k 2+E n k - y k 2 ε k 2 s k 2 n k y k 2 Since the input signal has no information about s k s k in it, minimizing E ε k 2 ε k 2 can only affect the second term, which is the standard Wiener filtering problem, with solution W= R n ' n ' -1 P n n ' W R n ' n ' P n n '

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