Fast multiresolution Gabor Transform based on synthesis of high frequency resolution spectrum from low frequency resolution spectra

In recent years, multiresolutional time-frequency analysis has been widely studied in many fields. However, multiresolution analysis requires a large amount of calculations in accordance with the number of resolutions. Recently, the signal become higher resolution, so it tends to increase the amount of computation further. Gabor Transform (GT) is well-known for minimizing the product of time and frequency resolution, and is often used for that analysis. In this paper, we propose a method that can reduce the complexity cost of GT. First, we propose that the spectrum of high frequency resolution can be synthesized from spectra of high time resolution. Next, we show the method of determining the parameters based on the acceptable synthesis error. Finally, we show the effect of complexity cost reduction. The proposed method achieved lower calculation complexity down to 62.9% maximum.