Abstract
The fractional Fourier transform (FrFT) plays an important role in analyzing the chirp signal. However, it fails in locating the local frequency contents which is required in some applications. Although the short-time Fourier transform (STFT) works well in locating the local frequency contents, it only has the fixed local resolution. However, S-transform (ST) not only locates frequency contents well, but also has frequency-dependent varying resolution. In this paper, the fractional S-transform (FrST), which connects the properties of both ST and FrFT and uniquely combines a frequency dependent resolution of the time-frequency space with absolutely referenced local fractional spectrum, is proposed. In addition, the optimal transform parameter for resolution analysis is also investigated. Its properties are presented as well. Examples are given to verify our proposed algorithm.
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