Next Gen Wavelets Down-sampling Preserving Statistics

摘要

We extend the 2~(nd) Gen Discrete Wavelet Transform (DWT) of Swelden to the Next Generations (NG) Digital Wavelet Transform (DWT) preserving the statistical salient features. The lossless NG DWT accomplishes the data compression of "wellness baseline profiles (WBP)" of aging population at homes. For medical monitoring system at home fronts we translate the military experience to dual usage of veterans & civilian alike with the following three requirements: (ⅰ ) Data Compression: The necessary down sampling reduces the immense amount of data of individual WBP from hours to days and to weeks for primary caretakers in terms of moments, e.g. mean value, variance, etc., without the artifacts caused by FFT arbitrary windowing, (ⅱ) Lossless: our new NG_DWT must preserve the original data sets, (ⅲ) Phase Transition: NG_DWT must capture the critical phase transition of the wellness toward the sickness with simultaneous display of local statistical moments. According to the Nyquist sampling theory, assuming a band-limited wellness physiology, we must sample the WBP at least twice per day since it is changing diurnally and seasonally. Since NG_DWT, like the 2~(nd) Gen, is lossless, we can reconstruct the original time series for the physicians' second looks. This technique of NG_DWT can also help stock market day-traders monitoring the volatility of multiple portfolios without artificial horizon artifacts.