Abstract

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.

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