Abstract
Signal reconstruction, especially for nonstationary signals, occurs in many applications such as optical astronomy, electron microscopy, and x-ray crystallography. As a potent tool to analyze the nonstationary signals, the linear canonical transform (LCT) describes the effect of quadratic phase systems on a wavefield and generalizes many optical transforms. The reconstruction of a finite discrete-time signal from the partial information of its discrete LCT and some known samples under some restrictions is presented. The partial information about its discrete LCT that we have assumed to be available is the discrete LCT phase alone or the discrete LCT magnitude alone. Besides, a reconstruction example is provided to verify the effectiveness of the proposed algorithm.
Highlights
Especially for nonstationary signals, plays an important role in optical signal processing and evokes considerable interest in these literatures.[1,2]. In many applications, such as optical astronomy,[3] electron microscopy, and x-ray crystallography,[4] it is desired to reconstruct a complete sequence from incomplete information about the signal
We present that a finite sequence can be completely reconstructed from its discrete linear canonical transform (LCT) magnitude or phase and some samples under some loosen restrictions
Zhang et al.: Signal reconstruction from partial information of discrete linear canonical transform matrices M1 and M2 are another LCT with the matrix M3 1⁄4 M2M1, and the inverse LCT is given by the LCT with parameters (d, −b, −c, a)
Summary
Especially for nonstationary signals, plays an important role in optical signal processing and evokes considerable interest in these literatures.[1,2] In many applications, such as optical astronomy,[3] electron microscopy, and x-ray crystallography,[4] it is desired to reconstruct a complete sequence from incomplete information about the signal. Works[5,6,7] on signal reconstruction have shown that a finite sequence can be uniquely specified by its FT magnitude with some samples under some restrictions. This reconstruction is based on an assumption that signals are band-limited in the Fourier domain. We present that a finite sequence can be completely reconstructed from its discrete LCT magnitude or phase and some samples under some loosen restrictions.
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