Fourier telescopy (FT) is an active imaging technology which interferes several spatial diverse, frequency-encoded laser beams on a distant target, and reconstructs the object image by demodulating the reflected time signals of intensity. A new approach of processing the time history of the reflected intensity for object reconstruction of FT is devised based on all-phase spectrum analysis. The phase and amplitude of the FT signals could be educed by all-phase fast Fourier tansform (apFFT) directly and exactly. Then, after eliminating unknown atmospheric phase errors by phase-closure algorithm, the object image could be reconstructed. Compared with the traditional approach, this method can avoid frequency errors of the reflected signals from objects, because the measurement of the phase and amplitude need not depend on the signal frequency. So, it is of great advantage to applying FT to fast moving targets, such as low earth objects (LEO), because the speed errors of the targets will lead to the frequency errors of the reflected signal, which will degrade the reconstruction. Another advantage of this method is that it can eliminate the piston jitter of atmospheric aberrations and the spectrum-shift errors of acoustic-optic modulators to a certain extent, which also leads to the frequency errors of signals. The feasibility of this method is verified by computer simulation. Compared with the traditional method in two situations: the signal with noise and with frequency errors, the new method has the great ability to eliminate the frequency error while not degrading its repression of noise.