Signal reconstruction from two close fractional Fourier power spectra

T. Alieva, M.J. Bastiaans, L. Stankovic

Research output: Chapter in Book/Report/Conference proceedingChapterAcademicpeer-review


Based on the definition of the instantaneous fre quency (signal phase derivative) as a local moment of the Wigner distribution, we derive the relationship between the instantaneous frequency and the derivative of the squared modulus of the fractional Fourier transform (fractional Fourier transform power spectrum) with respect to the angle parameter. We show that the angular derivative of the fractional power spectrum can be found from the knowledge of two close fractional power spectra. It per mits us to find the instantaneous frequency and to solve the phase retrieval problem up to a constant phase term, if only two close fractional power spectra are known. The proposed technique is noniterative and noninterferometric. The efficiency of the method is demonstrated on several examples including monocomponent, multicomponent, and noisy signals. It is shown that the proposed method works well for signal-to-noise ratios (SNRs) higher than about 3 dB. The appropriate angular difference of the fractional power spectra used for phase retrieval depends on the complexity of the signal and can usually reach several degrees. Other applica tions of the angular derivative of the fractional power spectra for signal analysis are discussed briefly. The proposed technique can be applied for phase retrieval in optics, where only the fractional power spectra associated with intensity distributions can be easily measured.
Original languageEnglish
Title of host publicationSelected Papers on Phase-Space Optics
EditorsM.E. Testorf, J. Ojeda-Castañeda, A.W. Lohmann
Place of PublicationBellingham
Number of pages12
ISBN (Print)0-8194-6353-1
Publication statusPublished - 2006

Publication series

NameSPIE Milestone series
VolumeMS 181


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