A non-supervised adaptive identification of unknown waveforms in the noisy environments is described in this paper. Adaptive correlating filter is proposed, which is constructed by means of linear combinations of orthogonal function filters. Its operation and statistical properties are stated in detail.
The output waveform of this filter represents the crosscorrelation function between the unknown waveform imbedded in noise and the impulse response waveform of this filter composed of linear combinations. By this result, this filter operates as follows. At the instant of the maximum value of cross-correlation function crossed over the threthold level, the combination weights are changed in accordance with the weighted average method so as to grow the filter output. If the above average process is repeated, it is numerically derived at large SN-ratio that the impulse response of this filter converges to the unknown waveform.
Finally the results obtained numerically and experimentally are discussed.