Decomposition of High-Order FIR Filters and Minimum-Phase Filter Design

In this study, the implementation of high-order FIR filter decomposition and minimum-phase filter design is investigated. One method is presented for decomposing arbitrary linear-phase FIR filters with distinct roots into the cascade of first-order, second-order and fourth-order subfilters. The other method is described for transforming nonrecursive filters with even-order, equal-ripple attenuation in the pass-band, stop-band and linear-phase into those with minimum-phase and half the degree, and again with equal-ripple attenuation in the pass-band and stop-band. The technique consists of quick and accurate polynomial root finding of the z -domain filter transfer function by searching a finite region in the complex z-plane, and separating the zeros in the complex z -domain. In FIR filter decomposition, the search of roots to determine the subfilter impulse response coefficients is restricted to distinct roots in four regions in the complex z -plane: on the real axis, on the unit circle, inside the unit circle and at (1, 0) or (-1, 0). In minimum-phase filter design, the search of roots is restricted in two categories: on the unit circle and inside the unit circle. In both methods, we used Lang’s root finding program to get the zeros of the FIR filter. Arbitrary FIR filters were designed and decomposed for all possible orders of subfilters. FIR filters with even-order, zero-phase and equal-ripple were designed and generated the half degree minimum-phase filters. Both methods have been tested on FIR filters with orders ranging to over 500 and have proven effective in decomposing filters to the cascade realization and designing minimum-phase filters

Finding Patterns in a Knowledge Base using Keywords to Compose Table Answers

We aim to provide table answers to keyword queries against knowledge bases. For queries referring to multiple entities, like "Washington cities population" and "Mel Gibson movies", it is better to represent each relevant answer as a table which aggregates a set of entities or entity-joins within the same table scheme or pattern. In this paper, we study how to find highly relevant patterns in a knowledge base for user-given keyword queries to compose table answers. A knowledge base can be modeled as a directed graph called knowledge graph, where nodes represent entities in the knowledge base and edges represent the relationships among them. Each node/edge is labeled with type and text. A pattern is an aggregation of subtrees which contain all keywords in the texts and have the same structure and types on node/edges. We propose efficient algorithms to find patterns that are relevant to the query for a class of scoring functions. We show the hardness of the problem in theory, and propose path-based indexes that are affordable in memory. Two query-processing algorithms are proposed: one is fast in practice for small queries (with small patterns as answers) by utilizing the indexes; and the other one is better in theory, with running time linear in the sizes of indexes and answers, which can handle large queries better. We also conduct extensive experimental study to compare our approaches with a naive adaption of known techniques.Comment: VLDB 201

On the minimum orbital intersection distance computation: a new effective method

The computation of the Minimum Orbital Intersection Distance (MOID) is an old, but increasingly relevant problem. Fast and precise methods for MOID computation are needed to select potentially hazardous asteroids from a large catalogue. The same applies to debris with respect to spacecraft. An iterative method that strictly meets these two premises is presented.Comment: 13 pages, 10 figures, article accepted for publication in MNRA