Determining the optimal order of fractional Gabor transform based on kurtosis maximization and its application

• Kurtosis maximization is used for searching optimal order of FrGT.
• KMFrGT algorithm is proposed and it is globally optimal transform.
• The KMFrGT can suppress the Gaussian noise for the advantages of kurtosis.
• Time–frequency resolutions of KMFrGT are higher than traditional analysis method.

The optimal order of fractional Gabor transform (FrGT) has a direct effect on the results of fractional time–frequency analysis. This paper uses kurtosis maximization (KM) method to determine optimal order of FrGT, which is more suitable for non-stationary signals, and the corresponding algorithm fractional Gabor transform based on kurtosis maximization (KMFrGT) is proposed. Comparing with the amplitude maximization (AM), KM gives more rational choice in determining the optimal order of FrGT. The distributions with large kurtosis have sharper peaks than distributions have small one, which helps KMFrGT to give globally optimal time–frequency representations; AM method for optimal order of FrGT may lead time–frequency results to a local optimum, multi-chirp and quadratic chirp signals are used to demonstrate the effectiveness. The KMFrGT can suppress the Gaussian noise for the advantages of kurtosis; single seismic record added Gaussian noise is used to test the idea. The resolution of KMFrGT is higher than the traditional Gabor transform, a simple method is proposed to compare the resolutions of two transforms. The real field seismic data application results show the good performance of KMFrGT in time–frequency analysis.