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Adaptive Interference (Noise) Cancellation

Module by: Douglas L. Jones. E-mail the author

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.
Figure 1
Figure 1 (fig1AdaptiveInter.png)

The object is to subtract out as much of the noise as possible.

Example 1: Engine noise cancellation in automobiles

Figure 2
Figure 2 (fig2AdaptiveInter.png)

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 .

Figure 3
Figure 3 (fig3AdaptiveInter.png)

Exercise 1

What conditions must we impose upon the microphone locations for this to work? (Think causality and physics!)

Analysis of the interference cancellor

Figure 4
Figure 4 (fig4AdaptiveInter.png)

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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