Abstract
It is shown that an adaptive system whose regressor is formed by tap delay-line (TDL) filtering of a multitone sinusoidal signal is representable as a parallel connection of a linear time-invariant (LTI) block and a linear time-varying (LTV) block. A norm-bound (induced 2-norm) is computed explicitly on the LTV block and is shown to decrease as N/sup -1/, where N is the number of taps. Hence, the adaptive system becomes in the limit as the number of taps goes to infinity. In the more realistic case where the number of taps N is finite, the new LTI plus norm-bounded perturbation representation renders, for the first time, the adaptive system analyzable by standard robust control methods.
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