Abstract
Hankel structures are widely employed in data analysis and signal processing. Not only Hankel matrices but also higher-order Hankel tensors arise frequently in disciplines such as exponential data fitting, frequency domain subspace identification, multidimensional seismic trace interpolation, and so on. As far as we know, the term “Hankel tensor” was first introduced by Luque and Thibon. Boyer et al. discussed the higher-order singular value decompositions (HOSVD) of structured tensors, including symmetric tensors, Hankel tensors, and Toeplitz tensors in more detail. Moreover, Papy et al. employed Hankel-type tensors in exponential data fitting. De Lathauwer also concerned the “separation” of signals that can be modeled as sums of exponentials (or more generally, as exponential polynomials) by Hankel tensor approaches. As for the properties of Hankel tensors, Qi recently investigated the spectral properties of Hankel tensor largely via the generating function. Song and Qi investigated the spectral properties of Hilbert tensors, which are special Hankel tensors.
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