We prove an ellitpical range theorem for the numerical range associated with SO(3). The geometry behind the elliptical range theorem is explained. The result is analogous to the well-known elliptical range theorem of the C-numerical range associated with U(2) or SU(2). We then apply the result to give some necessary conditions of the sharp points of the C-numerical range assoicated with SO(n) w...

We analyze the numerical range of high-dimensional random matrices, obtaining limit results and corresponding quantitative estimates in the non-limit case. For a large class of random matrices their numerical range is shown to converge to a disc. In particular, numerical range of complex Ginibre matrix almost surely converges to the disk of radius √ 2. Since the spectrum of non-hermitian random...

Techniques for the separate/joint optimization of error-feedback and realization are developed to minimize the roundoff noise subject to l2-norm dynamic-range scaling constraints for a class of 2-D state-space digital filters. In the joint optimization, the problem at hand is converted into an unconstrained optimization problem by using linearalgebraic techniques. The unconstrained problem obta...

This paper proposes a preamble structure for joint estimation of carrier frequency offset (CFO) and I/Q imbalance. Because existing methods cannot guarantee correct solutions within all range of CFOs, we derive two constraints of phase rotations applied to repetition patterns. By using the preamble based on the presented constraints, CFO is optimally estimated, and I/Q imbalance estimation is p...

Stampfli has shown that for a given T £ B(H) there exists a K £ C(H) so that o(T + K) = ow(T). An analogous result holds for the essential numerical range We(T). A compact operator K is said to preserve the Weyl spectrum and essential numerical range of an operator T £ B(H) if o(T + K) = o„(T) and W(T + K)= We(T). Theorem. For each block diagonal operator T, there exists a compact operator K wh...