Anandi Mahadevan

Multiscale Signal Processing with Discrete Hermite Functions

Discrete Hermite functions (DHf) provide a new way of analyzing digital signals. As opposed to cumbersome computational methods that can only construct orthogonal discrete Hermite functions effectively for a small number of indices, there is a new method of computing DHf that is fast and efficient. Signal processing techniques that have been applied using the continuous Hermite functions (CHf) can now be adapted to the digital case, using this orthonormal set of DHf that share many of the properties of the continuous CHf. For some time, a multiscale version of the CHf has been available for analysis and has been applied to different kinds of signals and shown to be related to receptive fields of neurons. In this chapter, we explore the application of the digital DHf in multiscale analysis, showing analogies to the multiscale analysis provided by the CHf.

Probabilistic characterization of sleep architecture: Home Based study on healthy volunteers

The quantification of sleep architecture has high clinical value for diagnostic purposes. While the clinical standard to assess sleep architecture is in-lab based polysomnography, higher ecological validity can be obtained with multiple sleep recordings at home. In this paper, we use a dataset composed of fifty sleep EEG recordings at home (10 per study participant for five participants) to analyze the sleep stage transition dynamics using Markov chain based modeling. The statistical analysis of the duration of continuous sleep stage bouts is also analyzed to identify the speed of transition between sleep stages. This analysis identified two types of NREM states characterized by fast and slow exit rates which from the EEG analysis appear to correspond to shallow and deep sleep respectively.