Three-dimensional linear prediction and its application to digital angiography
Multidimensional Systems and Signal Processing
Asymptotic spectral distribution of Toeplitz-related matrices
Fast reliable algorithms for matrices with structure
Toeplitz and circulant matrices: a review
Communications and Information Theory
Hyperspectral Data Exploitation: Theory and Applications
Hyperspectral Data Exploitation: Theory and Applications
Asymptotic optimal SINR performance bound for space-time beamformers
Signal Processing
A theorem on the asymptotic eigenvalue distribution ofToeplitz-block-Toeplitz matrices
IEEE Transactions on Signal Processing
An order-recursive algorithm to solve the 3-D Yule-Walker equationsof causal 3-D AR models
IEEE Transactions on Signal Processing
IEEE Transactions on Information Theory
Three-dimensional interferometric ISAR imaging for target scattering diagnosis and modeling
IEEE Transactions on Image Processing
| Hi-index | 35.68 |
In many detection and estimation problems associated with processing of second-order stationary random processes, the observation data are the sum of two zero-mean second-order stationary processes: the process of interest and the noise process. In particular, the main performance criterion is the signal-to-noise ratio (SNR). After linear filtering, the optimal SNR corresponds to the maximal value of a Rayleigh quotient which can be interpreted as the largest generalized eigenvalue of the covariance matrices associated with the signal and noise processes, which are block multilevel Toeplitz structured for m-dimensional vector-valued second-order stationary p-dimensional random processes Xi1,i2,....,ip ∈ Rm. In this paper, an extension of Szegö's theorem to the generalized eigenvalues of Hermitian block multilevel Toeplitz matrices is given, providing information about the asymptotic distribution of those generalized eigenvalues and in particular of the optimal SNR after linear filtering. A simple proof of this theorem, under the hypothesis of absolutely summable elements is given. The proof is based on the notion of multilevel asymptotic equivalence between block multilevel matrix sequences derived from the celebrated Gray approach. Finally, a short example in wideband space-time beamforming is given to illustrate this theorem.