In order to analyze the performance and characteristics of the Kronecker product measurement matrix, we apply the measurement matrix to a 2-D image acquisition simulation experiment and compare it with the Gaussian random matrix, Fourier matrix, Bernoulli matrix, Toeplitz matrix, polynomial matrix, and measurement matrix which are commonly used.
For the numerical solution to this problem we propose an algebraic approach, based on a fast factorization algorithm of the resulting Bezout matrix with polynomial entries, which avoids the need for symbolic computation.
Figure 1 Support of the window functions representable by matrices with maximal polynomial order P − 1 for J = 3, L = 4, P = 1, 2. The mapping of an input signal onto the signal at the output of a linear time-variant channel can be expressed as. (17).
In this paper, synthesis conditions are proposed in terms of parameter-dependent matrix inequalities with polynomial variables and a given scalar parameter.
Conceptual and numerical issues related to the spectral factorization of polynomials and polynomial matrices with complex coefficients are studied in this report.
The paper presents a new freely available library for symbolic computation with polynomial matrices.
The Polynomial Toolbox for Matlab version 2 (Polyx, 1999) is a new software package for computations with polynomial matrices.
The performance function minimization problem with polynomial matrix inequalities is then transformed into a problem of minimizing a convex performance function involving standard LMIs.
Simply speaking, the idea is to approximate the matrix inverse by a matrix polynomial with J terms, where J needs not to scale with the system dimensions to maintain a certain approximation accuracy [19].
However, we will show later in this article that in order to have compact order decomposition, phase alignment of decomposed constant matrices in DFT domain results in polynomial matrices with considerably lower order.
