4 bits/symbol Phase and Amplitude Modulation on a Single Discrete Eigenvalue for Transmissions based on Nonlinear Fourier Transform

2017 ◽  
Author(s):  
Tao Gui ◽  
Shun Ka Lo ◽  
Xian Zhou ◽  
Chao Lu ◽  
Alan Pak Tao Lau ◽  
...  
Keyword(s):  
Fourier Transform ◽  
Amplitude Modulation ◽  
Discrete Eigenvalue ◽  
Nonlinear Fourier Transform

scholarly journals Back-to-Back Performance of the Full Spectrum Nonlinear Fourier Transform and Its Inverse

Entropy ◽  
2020 ◽  
Vol 22 (10) ◽  
pp. 1131
Author(s):  
Benedikt Leible ◽  
Daniel Plabst ◽  
Norbert Hanik
Keyword(s):  
Fourier Transform ◽  
Numerical Simulations ◽  
Mean Squared Error ◽  
Detection Methods ◽  
Achievable Rate ◽  
Discrete Eigenvalue ◽  
Full Spectrum ◽  
Spectral Components ◽  
Discrete And Continuous Spectra ◽  
Nonlinear Fourier Transform

In this paper, data-transmission using the nonlinear Fourier transform for jointly modulated discrete and continuous spectra is investigated. A recent method for purely discrete eigenvalue removal at the detector is extended to signals with additional continuous spectral support. At first, the eigenvalues are sequentially detected and removed from the jointly modulated received signal. After each successful removal, the time-support of the resulting signal for the next iteration can be narrowed, until all eigenvalues are removed. The resulting truncated signal, ideally containing only continuous spectral components, is then recovered by a standard NFT algorithm. Numerical simulations without a fiber channel show that, for jointly modulated discrete and continuous spectra, the mean-squared error between transmitted and received eigenvalues can be reduced using the eigenvalue removal approach, when compared to state-of-the-art detection methods. Additionally, the computational complexity for detection of both spectral components can be decreased when, by the choice of the modulated eigenvalues, the time-support after each removal step can be reduced. Numerical simulations are also carried out for transmission over a Raman-amplified, lossy SSMF channel. The mutual information is approximated and the eigenvalue removal method is shown to result in achievable rate improvements.

Isolating solitons from the resonant continuous wave by using nonlinear Fourier transform

2021 ◽  
Author(s):  
Yutian Wang ◽  
Songnian Fu ◽  
Chi Zhang ◽  
Xiahui Tang ◽  
Jian Kong ◽  
...  
Keyword(s):  
Fourier Transform ◽  
Continuous Wave ◽  
Nonlinear Fourier Transform

scholarly journals Analytical and Numerical Investigation on the Duffing Oscilator Subjected to a Polyharmonic Force Excitation

2015 ◽  
Vol 45 (1) ◽  
pp. 3-16 ◽  
Author(s):  
Svetlin Stoyanov
Keyword(s):  
Fourier Transform ◽  
Analytical Solution ◽  
Discrete Time ◽  
Amplitude Modulation ◽  
Duffing Oscillator ◽  
Vibration Signal ◽  
Vibration Diagnostics ◽  
Significant Difference ◽  
Excitation Force ◽  
Force Excitation

Abstract An analytical solution for a specific case of the forced Duffing oscillator is proposed. The excitation force contains two harmonics with significant difference frequencies. This case corresponds to a presence of a defect in the machinery and is in the art of the machinery vibration diagnostics. The results obtained show an amplitude modulation. Therefore, the presence of an amplitude modulation in the vibration signal may be used as an indicator for a malfunction. Analytical solution derived clarifies how the amplitude modulation occurs. Also, a numerical solution is realized and compared with the analytical one. For this, the Duffing equation is solved numerically and then, the spectrograms of vibrations are obtained through a Discrete-time Fourier Transform.

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