Shrinivas Chimmalgi received his B. Tech in mechanical engineering from the National Inst. of Tech. Karnataka, India, in 2015 and his MSc. in systems and control from the TU Delft, Netherlands, in 2017. He is currently a PhD student in the Systems and Control department at TU Delft. His research is focused on numerical methods for nonlinear Fourier transform and its applications in fiber-optic communications.
NUMERICAL COMPUTATION OF NFTs
The idea of NFTs has been known for more than 40 years but its application to engineering has gained significant attention only in the past decade. Two emerging areas of application are fiber-optic communications and coastal engineering. The engineering applications rely on the ability to numerically compute NFTs in a reliable and efficient manner. However, unlike the now standard tool fast Fourier transform (FFT), there aren’t standard algorithms for computing NFTs. With the rise in attention towards NFTs, there has been much interest in numerical methods for NFTs which has led to some efficient numerical algorithms. In this talk I will first give the central ideas behind numerical methods for NFTs and then provide an overview of recent developments. I will concentrate on the NFTs associated with the nonlinear Schrödinger equation which is a model for the propagation of light in an ideal optical fiber. I will present details for the case of vanishing signals but also remark on how the methods can be extended to other boundary conditions and even other evolution equations. I will conclude by demonstrating how both forward and inverse NFT can be computed in under 40 lines of MATLAB code.