actual predictor characteristics is unnecessary. The problem considered here is prediction with two possible prediction delays. The desired signals are: (1) d("(n) = sin(2a/64(n + 311, and (2) d(')(n)= sin(2a/64(n +6)). The two versions of the desired outputs are associated with the U"'(n) = [000 011 1111 and U(2)( n ) = [ 11 1 100 0001 input patterns, respectively. During training, the input signal, the desired outputs, and the corresponding input patterns were repetitively applied. The

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... ng coefficients of the neural network were adjusted by using the on-line version of the backpropagation algorithm described by (31, (51, (7), and (8). Fig. 3 (b) shows the decrease of the average prediction error during the repetitive trials. It is important to note that during training, the neural network controlled resonator-bank structure learned the frequency characteristics of the two predictors and associated them with the corresponding input patterns. V. SUMMARY A new adaptive processing structure was presented in this paper. The neural network controlled resonator-bank structure offers an attractive alternative for implementing signal prqcessing and control systems whose dynamic characteristics have to be adjusted if changes are detected in the environment. An important feature of the proposed system is that the required behavior can be achieved by on-line training when a desired dynamic response is associated with patterns in observed signals. The first results of the experimental analysis of the structure are encouraging; the system is able to approximate a wide range of nonlinear dynamic behavior. ACKNOWLEDGMENT The author would like to thank the anonymous reviewers for their helpful comments and suggestions in making this paper more readable. REFERENCES Abstract -A simplified stability analysis of resonator-stabilized oscillators is carried out by using the describing function approach. On this basis a criterion for the evaluation and optimization of the frequency stabilization introduced in an oscillator by a resonating element with a large quality factor is proposed. In particular, a frequency-stabilization index, which can be conveniently used in the design of highly stable oscillators, is defined. The validity of this performance index has been verified in the design of microwave oscillators using dielectric resonators as frequency-stabilizing elements.