The Optimization of the Hermite transform: Application perspectives and 2D generalization

This paper studies the discrete Hermite transform applicability in concise representation of short-term and windowed sinusoidal signals. Namely, the Hermite functions show similar behavior with windowed multi-tone signals and filtered tones, which opens the possibility for signal sparsifation using an optimal transform scaling factor. In other words, the scaling factor is optimized in order to enhance the transform coefficients concentration. The scaling factor optimization method is based on concentration measures and it is further generalized to the case of 2D Hermite transform. Numerical examples illustrate the presented theoretical framework.