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The adaptive filter configurations that we have examined so far require a "desired signal" . There are many clever ways to obtain such a signal, but in some potential applications a desired signal issimply not available. However, a "property-restoral algorithm" can sometimes circumvent this problem.
If the uncorrupted signal has special properties that are characteristic of the signal and not of the distortion orinterference, an algorithm can be constructed which attempts to cause the output of the adaptive filter to exhibit thatproperty. Hopefully, the adapting filter will restore that property by removing the distortion or interference!
Certain communication modulation schemes, such as PSK and FSK,
transmit a sinusoid of a constant analytic magnitude. Only thefrequency or phase change with time. The constant modulus
algorithm tries to drive the output signal to one having aconstant amplitude:
One can derive an LMS (or other) algorithm that seeks a Wiener
filter minimizing this error. In practice, this works verywell for equalization of PSK and FSK communication channels.
This property-restoral idea can be used in any context in which a property-related error can be defined.
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