Signal extrapolation from Hartley transform magnitudes

Abstract

A novel approach to the problem of signal extrapolation from its Hartley transform magnitudes is presented. Using a newly defined function, it is proved that using only one known sample and the associated Hartley transform magnitudes a finite extended signal can be completely reconstructed. An algorithm for signal reconstruction from short-time Hartley transform (STHT) magnitudes with minimal window overlap can consequently be derived.

Detailed analysis of inverse Fourier transform techniques to uniquely infer second-order nonlinearity profile of thin films

“…11 Several algorithms have been developed to achieve such a recovery. [11][12][13] Since d S1 ͑z͒ is a real and odd function, all algorithms conveniently involve only half of the frequency spectrum. The recovered profile d S1 ͑z͒ is also an odd function, and either its z Ͻ 0 or z Ͼ 0 portion is equal to the nonlinearity profile d A ͑z͒ = d B ͑z͒.…”