Fast Gabor Transformation For Processing High Quality Audio

The Gabor transformation with a Gaussian window has several advantages over classical short time transformations such as the windowed FFT and wavelets. It allows for perfect localization in time and frequency according to the absolute bound expressed by the Heisenberg uncertainty principle. Furthermore the time-frequency resolution can be chosen as desired. This is bought dearly by the necessity of oversampling and very large windows resulting in high computational and storage costs. To overcome this disadvantages the FFT can be used as an underlying technique to speed up the computation for some rare dedicated time-frequency resolutions. In this paper the use of the FFT is extended to allow choosing the time-frequency resolution arbitrarily, by introducing only a small computational overhead. With the same approach we show, how to use the FFT to compute the Gabor transformation on non-separable lattices. The speed-up factors over an optimized DFT approach range from 2.5 to 100