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

Multiwindow discrete Gabor transform (M-DGT) is applied to present the Gabor time–frequency representation for transient signals (exponentially damped sinusoidal signals) with high time–frequency resolution. Due to the limitation of the constrained time–frequency 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.