A possible use of Fourier Transform analysis method as a distance estimator

We speculate on the possibility of using the Fourier transform analysis method as a distance estimator of the observed gamma-ray bursts (GRBs). It is based on a hypothetical empirical relation between the redshift and the power-law index of power density spectra (PDSs) of the observed GRBs. This relation is constructed by using the fact that the observed power-law index is dependent upon a characteristic timescale of GRB light curves. The rms error of redshift estimates is 0.42 for an empirical relation obtained with the 7 long () GRBs observed by the BATSE whose redshift information is available. We attempt to determine the spatial distribution of the GRBs observed by the BATSE as a function of redshifts on the basis of the resulting redshift estimator. We discuss possible uncertainties of the suggested method.