Geodesic
Several observations on Toeplitz and Hankel circulants
Zapiski Nauchnykh Seminarov POMI, Computational methods and algorithms. Part XIX, Tome 334 (2006), pp. 121-127 Cet article a éte moissonné depuis la source Math-Net.Ru

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An application of the unitary similarity with the discrete Fourier transform to the algebra of diagonal matrices yields the algebra of circulants. It turns out that if, in this construction, the unitary similarity is replaced by the unitary congruence, then the class of the so-called Hankel circulants is obtained. The causes and certain effects of this fact are discussed. 
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Kh. D. Ikramov; V. N. Chugunov. Several observations on Toeplitz and Hankel circulants. Zapiski Nauchnykh Seminarov POMI, Computational methods and algorithms. Part XIX, Tome 334 (2006), pp. 121-127. http://geodesic.mathdoc.fr/item/ZNSL_2006_334_a8/

[1] E. Bozzo, “Algebras of higher dimension for displacement decompositions and computation with Toeplitz plus Hankel matrices”, Linear Algebra Appl., 230 (1995), 120–150 | DOI | MR

[2] V. V. Voevodin, E. E. Tyrtyshnikov, Vychislitelnye protsessy s teplitsevymi matritsami, Nauka, M., 1987 | MR | Zbl