State Space Reconstruction

If the source of the signal were an autonomous linear system, looking at the frequency spectrum of the signal would be utmost informative, thus the Fourier domain would be an appropriate space to examine the signal. If the linear system had an explicit time component hosting some burst of high frequency events localized in time domain, then a linear transform, such as wavelet transform, would be useful. Much of the contemporary signal processing toolkits (e.g. Matlab [373]) are based on the ability to perform a linear transformation that converts a low-order ordinary differential equation to another domain, and perform matrix manipulations on the transformed algebraic representation of the measurements.

In the case of a nonlinear source, we are not likely to find any simplification from using a linear transformation, such as Fourier, since the processes that give rise to chaotic behavior are fundamentally multivariate. Consequently, we need to reconstruct the (multidimensional) state-space of

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