In many situations, the statistics of the noise which corrupts a signal are not known a priori, or the power of the noise is overwhelmingly greater than the power of the desired signal. In these circumstances, we cannot use traditional filtering techniques such as Weiner filtering. However, if it is possible to make a separate recording of the noise alone, we can use an adaptive technique to improve the signal.

One application of this adaptive noise cancellation is in the pilot's radio headset in jet aircraft. A jet engine can produce noise levels of over 140 dB. Since normal human speech occurs between 30 and 40 dB, it is clear that traditional filtering techniques will not work. To implement an adaptive technique, we place an additional microphone at the rear of the aircraft to record the engine noise directly. By taking advantage of the additional information this reference microphone gives us, we can substantially improve the signal from the pilot.

A naive approach to implement such noise cancellation would be to directly subtract the reference noise signal from the primary signal. However, this technique will not work, because the noise at the reference microphone will not be exactly the same as the noise at the primary microphone. There will be a delay corresponding to the distance between the primary and reference microphones. Also, unknown acoustic effects, such as an echoes or low pass filtering, can occur to the noise as it travels through the fuselage of the aircraft. Even in the ideal case, the delay alone will guarantee that simply subtracting will not properly cancel the noise.

If we model the path from the noise source to the primary microphone as a linear system, we can devise an adaptive algorithm to train an FIR filter to match the acoustic characteristics of the channel. If we then apply this filter to the noise recorded at the reference microphone, we should be able to successfully subtract out the noise recorded at the primary microphone. This leaves us with an improved recording of the pilot's voice.

Next we look at two algorithms we can use to train the FIR filter, Algorithms.