Density estimation and wavelet thresholding via Bayesian methods: a wavelet probability band and related metrics to assess agitation and sedation in ICU patients

A wave is usually defined as an oscillating function that is localized in both time and frequency. A wavelet is a “small wave”, which has its energy concentrated in time providing a tool for the analysis of transient, non-stationary, or time-varying phenomena. Wavelets have the ability to allow simultaneous time and frequency analysis via a flexible mathematical foundation. Wavelets are well suited to the analysis of transient signals in particular. The localizing property of wavelets allows a wavelet expansion of a transient component on an orthogonal basis to be modelled using a small number of wavelet coefficients using a low pass filter. This wavelet paradigm has been applied in a wide range of fields, such as signal processing, data compression and image analysis.