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I am working with Toeplitz matrix, I know that a Toeplitz Matrix $T$ can be decompose as a sum of a circulant and skew circulant matrix which can be diagonalized using the DFT matrix

$T=C+S = F\Lambda_C F^H + DF\Lambda_S F^HD^H$

where D is $D=\text{diag}(exp(j\frac{\pi}{N}n)) n=0,...,N-1$.

My question is if we can obtain efficiently the eigenvalues and eigenvectors of the following matrix efficiently

$F^HTF=\Lambda_C + F^HDF\Lambda_SF^HD^HF$

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