Decimal Operations Research Articles

Novel multirate processing of beamspace noise eigenvectors

A novel implementation of Root-MUSIC is introduced based on the observation that the MUSIC null spectrum created with a beamspace noise eigenvector is bandpass exhibiting nulls at the locations of in-band sources. Thus, after telescoping to element space and modulating to broadside, the telescoped noise eigenvector may be decimated yielding a small order polynominal with the separation between signal roots increased by the decimation factor. Depending on the out-of-band response of the beamformers, the telescoped noise eigenvector may be passed through a lowpass filter prior to decimation to preserve in-band source nulls. A low cost algorithm is realized by invoking linearity and performing the modulation, filtering, and decimation operations a priori on the beamformers yielding a simple transformation to be applied to the beamspace noise eigenvectors. >

Factorization of Polynomials over Finite Fields and Characteristic Sequences

A new factorization algorithm for polynomials over finite fields was recently developed by the first author. For finite fields of characteristic 2, it is known from previous work that this algorithm has several advantages over the classical Berlekamp algorithm. In this paper we show that the linearization step in the new algorithm is feasible—in the sense that it can be carried out in polynomial time—for arbitrary finite fields, by using an approach based on decimation operators and characteristic linear recurring sequences. We also introduce a general principle for the linearization of the factorization problem for polynomials over finite fields.

Electronic states on a fractal: Exact Green's-function renormalization approach.

A nontrivial tight-binding model for electron dynamics on the fractal Koch curve is investigated within the framework of the Green's-function formalism. The key result is the construction of a multiple exact renormalization group that allows one to derive all the rather unusual properties of the model. This group is generated by four nonequivalent decimation operations, which define distinct transformation rules for the 48 relevant parameters to be renormalized. The calculation of the density of states confirms the crucial results that were obtained recently using transfer-matrix methods: local self-affinity, dense gap structure, and singular electronic levels with infinite degeneracy. This demonstrates that the Green's-function approach is not inferior to other techniques even in topologically one-dimensional situations.

Spectral line estimation using complex coefficient prefilters

AbstractA spectral line estimation method is proposed which improves the resolution of the two nearby sinusoidal frequencies. In contrast to the conventional method in which the decimation operation is applied to the signal passing through the real coefficient bandpass prefilter, the present method carries out the process by means of the complex coefficient prefilter. By means of this technique, numerous problems to be resolved under the condition that relatively few data are given under a low SN ratio, such as the problem of initial phase dependence and the problem of accurate spectral estimation at a low‐ or high‐frequency region, can be overcome.This paper presents a method in which the decimated signals by a decimation operation are used effectively. The method particularly improves the estimation capability in the case with fewer data. Finally, by means of a simulation, the effectiveness of these methods is proven. It is shown that the estimation accuracy is improved significantly as long as the amount of operations is similar to that for the conventional method using the real coefficient prefilter.