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A minimal generalized time-bandwidth product-based coarse-to-fine strategy is proposed with one novel ideas highlighted: adopting a coarse-to-fine strategy to speed up the searching process. The simulation results on synthetic and real signals show the validity of the proposed method.

To get a high resolution time-frequency distribution, fractional Fourier transform (FrFT) is a useful tool. Traditional time-frequency method combined FrFT, and fractional Gabor transform was proposed [

Fractional Fourier transform (FrFT) is a generalization of the Fourier transform, FrFT is a linear operator. The FrFT of signal can be interpreted as the rotating the signal in the time-frequency plane, the FrFT of

where

where

In light of the properties of the FrFT, the interval of the optimum order can be restricted in [0, 2) [

If the p-th order FrFT of signal

where

where

where

where

where

The optimum order of FrFT can be given by minimal generalized time-bandwidth product:

According to the operation properties of FrFT, the order of FrFT can be narrowed to the range of

Suppose

Step 1:

Step 2: let

Step 3: perform FrFT of the signal for each

Step 4: Find

Step 5:

The above loops can be stopped until the number of cycles equals to the number M:

where

Suppose an N points signal

The MGTBP is implemented for searching the optimum order of FrFT, the fast discrete FrFT algorithm is reported by Ozakatas et al. [

The parameter settings take the values as follows:

In this paper, the MGTBP method for estimating the optimum fractional Fourier order has been developed. Its computational complexity is

The authors wish to thank the National Natural Science Foundation of China (Grants No. 41274127) and the Yili Normal University research project (Grants No. 2014YSYB04) for financial support of this research.

Lin Tian,Zhenming Peng, (2015) Minimal Generalized Time-Bandwidth Product Method for Estimating the Optimum Fractional Fourier Order. Journal of Computer and Communications,03,8-12. doi: 10.4236/jcc.2015.33002