Nonlinear Fourier transform of time-limited and one-sided signals

Vishal Vaibhav

Research output: Contribution to journalArticleScientificpeer-review

4 Citations (Scopus)
20 Downloads (Pure)


In this article, we study the properties of the nonlinear Fourier spectrum in order to gain better control of the temporal support of the signals synthesized using the inverse nonlinear Fourier transform. In particular, we provide necessary and sufficient conditions satisfied by the nonlinear Fourier spectrum such that the generated signal has a prescribed support. In our exposition, we assume that the support is a simply connected domain that is either a bounded interval or the half-line, which amounts to studying the class of signals which are either time-limited or one-sided, respectively. Further, it is shown that the analyticity properties of the scattering coefficients of the aforementioned classes of signals can be exploited to improve the numerical conditioning of the differential approach of inverse scattering. Here, we also revisit the integral approach of inverse scattering and provide the correct derivation of the so called Töplitz inner-bordering algorithm. Finally, we conduct extensive numerical tests in order to verify the analytical results presented in the article. These tests also provide us an opportunity to compare the performance of the two aforementioned numerical approaches in terms of accuracy and complexity of computations.

Original languageEnglish
Article number425201
Number of pages34
JournalJournal of Physics A: Mathematical and Theoretical
Issue number42
Publication statusPublished - 2018

Bibliographical note

Accepted Author Manuscript


  • integrable nonlinear partial differential equation
  • inverse scattering
  • nonlinear optics


Dive into the research topics of 'Nonlinear Fourier transform of time-limited and one-sided signals'. Together they form a unique fingerprint.

Cite this