Gabor multipliers are an efficient tool for time variant filtering used implicitly in many engineering applications in signal processing. For these operators, the result of a Gabor transform (the sampled version of the Short Time Fourier Transform) is multiplied by a fixed function, called the time-frequency mask or symbol. The result is then synthesized.
While Gabor multipliers are widely and practically used, some of their theoretical properties are not well known. The goal of this project is to improve the mathematical knowledge about Gabor multipliers, in order to optimize their use in applications.
The problem will be approached using modern Gabor theory, harmonic analysis tools, and numeric tools. Formulation and demonstration of analytical statements will be conducted jointly with systematic numeric experiments to study the properties of Gabor multipliers.
The following topics will be investigated in the project:
The applications of Gabor multipliers in signal processing are numerous, and include any application requiring time-variant filtering. Some applications of Gabor multipliers will be investigated further in the following parallel projects:
The implementation of a Gabor multiplier in the software system STx has already proceeded quite far, see Stx-Mulac.