A single unifying algorithm has been developed to systematize the collection of compact Daubechies wavelets. This collection comprises all classes of real and complex orthogonal and biorthogonal wavelets with the maximal number K of vanishing moments for their finite length. Named and indexed families of wavelet filters were generated by spectral factorization of a product filter in which the optimal subset of roots was selected by a defining criterion within a combinatorial search of subsets meeting required constraints. Several new families have been defined some of which were demonstrated to be equivalent to families with roots selected solely by geometric criteria that do not require an optimizing search. Extensive experimental results are tabulated for 1 # K # 24 for each of the families and most of the filter characteristics defined in both time and frequency domains. For those families requiring optimization, a conjecture for K>24 is provided for a search pattern t...

This paper brings steps 3 and 4 near to completion, building on the Kateb -- Lemarie analysis of step 2. The phase is of crucial importance because orthogonal filters cannot be symmetric ( beyond the Haar case p 1 ) . We show that the filter coefficients and the scaling functions have similar asymptotic behavior ( but not identical! See Section 6 ) . The zeros of H 70 (z) are shown in Fig. 1. There are 70 zeros at z or v p, which makes the function "maxflat." The other 69 zeros are inside the unit circle, which makes it "minphase." The graph of H 70 (v) shows that the filter is "lowpass "; the magnitude is near zero for high frequencies. This graph approaches the ideal one-zero function as p r ` . Then the magnitude of the infinite product ) approaches the characteristic function of [0p, p]

Effective management of device-supported patients in the Intensive Care Unit (ICU) is complex, involving the interpretation of large volumes of high frequency data from numerous cardiac and respiratory parameters presented by the ICU monitors. ICU Clinical Decision Support systems can play an important role in assisting medical staff in terms of its ability to disentangle and comprehend large amount of physiological datasets with a number of explanatory variables. We propose data wavelets as a data mining approach for analyzing historical ICU data for deriving trends. We propose a clinical decision support system that uses the trends to assist medical staff by performing temporal reasoning to determine the outcome of therapies and to reason qualitatively to remove clinically insignificant events and to identify clinical conditions.. Keywords signal processing, medicine, time-series analysis, data mining, wavelets. 1.

Broadband is the common form of telecommunication used for Intensive Care Unit (ICU) telemedicine. However, in rural areas, bandwidth demand can easily outstrip the revenue realizable that is needed to pay for the network infrastructure investment so lower bandwidth is normal. A consequence of restricted bandwidth on access pipes is service contention at the customer site. To address these challenges we need to consider Quality of Service issues before we can successfully deploy a successful ICU telemedicine system. Quality of Service refers to the set of technologies and techniques for managing network traffic with the goal of providing a certain level of performance to a data flow in a network. In this paper we will discuss how the use of data wavelets as a form of data compression of ICU data makes for better use of broadband in rural areas and, in turn, improves Quality of Service in telemedicine.