Abstract: Wavelets have a tremendous ability to extract signals from noisy environments. However, the use of wavelets can be computationally expensive. The number of computations increases with the size of the wavelet family. Here a wavelet family is combined into a single complex-valued signal that can then be used to extract information form an input signal. The advantage is that the expense of computation is that of a single correlation rather than the several correlations required by the wavelet family. This new filter is constructed using a phase-encoded fractional power filter and offers the user the option of manipulating the trade-off generalization and discrimination that is inherent in first-order filtering. The result is a computationally cheaper method of using wavelets to detect signals embedded in noise. !3
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