Synthesis of Real Weyl-Heisenberg Signal Frames with Desired Frequency-Time Localization

• Main Authors: Valery Volchkov, Vladimir Sannikov, Alexander Mamonov
• Format: Article
• Language: English
• Published: FRUCT 2019-04-01
• Series: Proceedings of the XXth Conference of Open Innovations Association FRUCT
• Subjects: Weil-Heisenberg frame; optimal tight frame; desired frequency-time localization; effective computational implementation
• Online Access: https://fruct.org/publications/fruct24/files/Vol.pdf

An algebraic approach to the synthesis of optimal real Weyl-Heisenberg frames with the best frequency-time localization oriented to the processing of discrete signals is developed. The chosen optimality criterion ensures the construction of a tight signal frame with the lowest standard deviation of frame functions from the desired standard. In addition, a special algebraic structure of the synthesis algorithm in the form of a product of sparse matrices allows for efficient computational implementation and flexible adjustment of the frequency-time resolution of the signal functions of the frame. The results of the experiment confirming the effective computational implementation of the algorithm and a desired time-frequency localization of frame functions are presented.