Elimination of exponential interference form finite-length discrete signals

A method for removing exponential interference from discrete, finite-length signals is presented. The removal of the sine-wave interference is comparable to a sharp notch filter, but without transient effects. In addition, it is found that matrices, when multiplied with a vector of samples of any given signal, completely eliminate from it an exponential interference that satisfies a given homogeneous difference equation (HDE). All other components of the given signal (which are orthogonal to the solutions of that HDE) are unaffected.<
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