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

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.