Signal reconstruction from two close fractional fourier power spectra

Signal reconstruction from two close fractional Fourier power spectra

Based on the definition of the instantaneous frequency (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 fra...

On Signal Reconstruction from Fourier Magnitude

In this paper, three new algorithms for signal reconstruction from spectral magnitude are presented. The first algorithm reconstructs a signal from its discrete Fourier transform (DFT) magnitude and half of its samples using the decimation-in-time FFT algorithm, which results in a closed-form solution for the unknown data. The second is based on localized Fourier transform magnitudes and a sing...

Signal reconstruction from Fourier transform sign information

Phase Reconstruction from Two Wigner Distribution Projections

The connection between the instantaneous frequency and the angle derivative of the fractional power spectra is established. It permits to solve the signal retrieval problem if only two close fractional power spectra are known. This fact is used in the reconstruction of the Wigner distribution or the pseudo Wigner distribution from two close projections. Keywords—Wigner distribution, fractional ...

Complex signal recovery from multiple fractional Fourier-transform intensities.

The problem of recovering a complex signal from the magnitudes of any number of its fractional Fourier transforms at any set of fractional orders is addressed. This problem corresponds to the problem of phase retrieval from the transverse intensity profiles of an optical field at arbitrary locations in an optical system involving arbitrary concatenations of lenses and sections of free space. Th...