Noise cancellationNoise cancellation

Bui Le SonVo Phuc Luan

11ECE2

AssumptionAssumptionAssume that we have a input signal:

x(n) = d(n) + v1(n)

With d(n) is signal source and v1(n) is noise source.

We want to remove the noise v1(n), we use a sensor to record the noise v2(n),which is the input to the Wiener filter that is used to estimate the noise v1(n), the Wiener-Hopf equation are:

Rv2w = rv1v2

Derive W-H solutionDerive W-H solutionWe consider the same data model as for

filtering: x(n) = d(n) + v1(n) or x = d + v1

where d = [d(n), . . . , d(n − p + 1)]T

and v1 = [v1(n), . . . , v1(n − p + 1)]T .

This time we estimate v1(n) from a correlated noise source v2(n), and estimate d(n) as

dˆ(n) = x(n) − v1ˆ(n) with

v1ˆ(n) = wTv2

where v2 = [v2(n), . . . , v2(n − p + 1)]T .

To estimate v1(n) from v2(n), we start from the Wiener-Hopf equations

Rv2w = rv1v2

Since rv1v2 is generally not known, we can rewrite this as

rv1v2 = E{v1(n)v2*} = E{(d(n) + v1 (n)) v2

*} = E{x(n) v2

*} = rxv2

and thus the Wiener-Hopf equations can be written as

Rv2w = rxv2

As already mentioned, d(n) is then estimated as

dˆ(n) = x(n) − v1ˆ(n) with v1ˆ(n) = wTv2

ExampleExample

ExampleExample

ProblemProblem

MATLABMATLABDescription: This on of the project that shows

how to implement Wiener filter as noise cancellations. Our desired response is d(n) output is x(n). We have noise v(n), v1(n) and v2(n) that have the following relationship v1(n)= 0.8*v1(n-1)+v(n) and

v2(n)= -0.6v2(n-1)+v(n)

where v(n) is AWGN.

The ouptut is x(n)=d(n)+v1(n)

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ConclusionConclusionThis method is useful is in air-to-air communications between pilots in fighter aircraft or in air-to-ground communication between a pilot and a control tower. Since there is often a large amount of engine and wind noise within the cockpit of the fighter aircraft, communication is often a difficult problem. However , if a secondary microphone is placed within the cockpit of an aircraft, then one may estimate the noise that is transmitted when the pilots speaks into microphone, and subtract this estimate from the transmitted signal, thereby increasing the signal-to-noise- ratio.