Gabor time-frequency representation for transient signals using multiwindow discrete Gabor transform

Multiwindow discrete Gabor transform (M-DGT) is applied to present the Gabor timefrequency representation for transient signals (exponentially damped sinusoidal signals) with high time-frequency resolution. Due to the limitation of the constrained timefrequency localization governed by the Heisenberg uncertainty principle, using a wider analysis window in time domain will lead to the Gabor time-frequency spectrum (or representation) with higher frequency resolution but poor time resolution for the transient signals, and using a narrower analysis window in time domain will result in the Gabor time-frequency spectrum (or representation) with higher time resolution but poor frequency resolution for the transient signals. To obtain the Gabor time-frequency representation with both higher frequency resolution and higher time resolution, the above two spectra can be combined by geometric average. The experimental results show that the combined Gabor time-frequency representation for the transient signals has higher time-frequency resolution than that obtained when only the single analysis window is used in the traditional discrete Gabor transform.