Channels with spectral nulls are sometimes dubbed bad channels because they can cause poor performance in communication systems. This correspondence investigates the validity of this intuition by studying the geometry of an orthogonal frequency-division multiplex (OFDM) system. It is shown that the subchannel attenuation coefficients form a natural coordinate system for describing finite-impuls...

This paper concerns the structure that can be achieved by feedback in descriptor systems that lack controllability at innnity. Staircase and double staircase condensed forms obtained through a sequence of orthogonal state transformations display when and how feedback can be used to achieve minimal index. Furthermore, they reveal that the modes that are uncontrollable at innnity have a xed minim...

In this article, we consider the decoding problem of Grassmann codes using majority logic. We show that for two points Grassmannian, there exists a canonical geodesic between these once complete flag is fixed. These geodesics are used to construct large set parity checks orthogonal on coordinate code, resulting in algorithm.

An edge-unfolding of a polyhedron is produced by cutting along edges and flattening the faces to a net, a connected planar piece with no overlaps. A grid unfolding allows additional cuts along grid edges induced by coordinate planes passing through every vertex. A vertexunfolding permits faces in the net to be connected at single vertices, not necessarily along edges. We show that any orthogona...

This paper presents two new sets of nonseparable discrete orthogonal Charlier and Meixner moments describing the images with noise and that are noise-free. The basis functions used by the proposed nonseparable moments are bivariate Charlier or Meixner polynomials introduced by Tratnik et al. This study discusses the computational aspects of discrete orthogonal Charlier and Meixner polynomials, ...

An orthogonal hyperprismatic grid whose all nodes are accompanied by the given function values can not be generally constructed due to the random nature of the given function data. This prevents the reduction of the single multivariate interpolation to more than one univariate or bivariate interpolations even approximately. It is generally quite difficult to determine an analytical structure fo...

One design for three-dimensional multimicrophone probes is the four-microphone orthogonal design consisting of one microphone at an origin position with the other three microphones equally spaced along the three coordinate axes. Several distinct processing methods have been suggested for the estimation of active acoustic intensity with the orthogonal probe; however, the relative merits of each ...

Circuits to achieve geometric transformations including two-point swapping, flip, coordinate swapping, orthogonal rotations and their variants on N-sized quantum images are proposed based on the basic quantum gates; NOT, CNOT and Toffoli gates. The complexity of the circuits is O(log N) for two-point swapping and O(log N) for flip, co-ordinate swapping and orthogonal rotations. The results indi...

This paper introduces a new set of orthogonal moment functions based on the discrete Tchebichef polynomials. The Tchebichef moments can be effectively used as pattern features in the analysis of two-dimensional images. The implementation of moments proposed in this paper does not involve any numerical approximation, since the basis set is orthogonal in the discrete domain of the image coordinat...