A new way for reversible Tau-P transform by FFT

Based on the Fourier Slice Theorem, through analyzing the physical significances of the DFT and the relationship between the DFT and the FFT, this paper proposed a new way for implementing the Tau-P transform by the FFT. By comparison with other existing ways, the mainly difference of the forward process is to directly convert signal from f-x domain to f-p domain other than from f-x domain to f-k domain and then through interpolation and coordinate transform to f-p domain, and the inverse process is converse. Otherwise, two points need to be considered, the first is that the number for the FFT on the process from f-x domain to f-p domain is variable with the frequency sample. The bigger the frequency is, the smaller the number for the FFT. The second is that the background energy should be recalled for faithfully reconstructing the copy of the original data. Through the example testing, the new Tau-P transform proposed here is the reversible process. Meanwhile, the new way is faster since its three steps all implemented by FFT, no interpolation and coordinate conversion like other ways.