The recursive Walsh transform.

概要

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A recursive algorithm for calculating the Walsh coefficients (Recursive Walsh Transform; RWT below) is developed. The proposed algorithm updates the Walsh coefficients being previously calculated using the past 2n time-series data, by the consecutively sampled datum. The software based on the proposed algorithm is composed and demonstrated. The execution time of one step (updates the Walsh coefficients one time) is faster than the FWT's about four times. A method of calculating a consistent Walsh power spectra based on the proposed RWT algorithm is also presented and demonstrated. Finally time-variant sequency of the input data is estimated step by step using the RWT algorithm. The result is that the real-time computing procedures based on the RWT algorithm estimates the value of the time-variant sequency accurately with the delay of only two or three periods of input data provided that the values of the involved weighted coefficients are appropriately assigned.
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