Stability of Frames Generated by Nonlinear Fourier atoms

Quadrature signal processing is used in many fields of science and engineering, and quadrature signals are necessary to describe the processing and implementation that takes place in modern digital communication systems. It serves two purposes: to determine the parameters needed for the construction of a necessary model, and to confirm if the model constructed represents the physical phenomenon. Especially nowadays, with the development of science and technology, a large amount of data is waiting for further scientific exploration. Traditional data analysis methods such as Fourier analysis, based on the linear stationary assumption have been shown to be efficient for processing of linear and stationary data. However, data from real systems, either natural or man-made ones, are most likely to be both nonlinear and non-stationary. Many studies have shown that the traditional data analysis methods are not suitable for analyzing nonlinear and non-stationary data. Only in recent years have new methods been introduced to analyze non-stationary and nonlinear