Factorability of lossless time-varying filters and filter banks

We study the factorability of linear time-varying (LTV) lossless filters and filter banks. We give a complete characterization of all, degree-one lossless LTV systems and show that all degree-one lossless systems can be decomposed into a time-dependent unitary matrix followed by a lossless dyadic-based LTV system. The lossless dyadic-based system has several properties that make it useful in the factorization of lossless LTV systems. The traditional lapped orthogonal transform (LOT) is also generalized to the LTV case. We identify two classes of TVLOTs, namely, the invertible inverse lossless (IIL) and noninvertible inverse lossless (NIL) TVLOTs. The minimum number of delays required to implement a TVLOT is shown to be a nondecreasing function of time, and it is a constant if and only if the TVLOT is IIL. We also show that all IIL TVLOTs can be factorized uniquely into the proposed degree-one lossless building block. The factorization is minimal in terms of the delay elements. For NIL TVLOTs, there are factorable and unfactorable examples. Both necessary and sufficient conditions for the factorability of lossless LTV systems are given. We also introduce the concept of strong eternal reachability (SER) and strong eternal observability (SEO) of LTV systems. The SER and SEO of an implementation of LTV systems imply the minimality of the structure. Using these concepts, we are able to show that the cascade structure for a factorable IIL LTV system is minimal. That implies that if a IIL LTV system is factorable in terms of the lossless dyadic-based building blocks, the factorization is minimal in terms of delays as well as the number of building blocks. We also prove the BIBO stability of the LTV normalized IIR lattice

One- and two-level filter-bank convolvers

In a recent paper, it was shown in detail that in the case of orthonormal and biorthogonal filter banks we can convolve two signals by directly convolving the subband signals and combining the results. In this paper, we further generalize the result. We also derive the statistical coding gain for the generalized subband convolver. As an application, we derive a novel low sensitivity structure for FIR filters from the convolution theorem. We define and derive a deterministic coding gain of the subband convolver over direct convolution for a fixed wordlength implementation. This gain serves as a figure of merit for the low sensitivity structure. Several numerical examples are included to demonstrate the usefulness of these ideas. By using the generalized polyphase representation, we show that the subband convolvers, linear periodically time varying systems, and digital block filtering can be viewed in a unified manner. Furthermore, the scheme called IFIR filtering is shown to be a special case of the convolver

PROJECT OPTIMA: optimisation of policies for transport integration in metropolitan areas

The overall objectives of Project OPTIMA were: (i) to identify optimal urban transport and land use strategies for a range of urban areas within the EU; (ii) to compare the strategies which are specified as optimal in different cities, and to assess the reasons for these differences; (iii) to assess the acceptability and feasibility of implementation of these strategies both in nine case study cities (Edinburgh, Merseyside, Vienna, Eisenstadt, Tromsø, Oslo, Helsinki, Torino and Salerno) and more widely in the EU; and (iv) to use the results to provide more general guidance on urban transport policy within the EU

A Presheaf Interpretation of the Generalized Freyd Conjecture

We give a generalized version of the Freyd conjecture and a way to think about a possible proof. The essential point is to describe an elementary formal reduction of the question that holds in any triangulated category. There are no new results, but at least one known example drops out quite trivially.Comment: 8 pages; formerly titled "Thinking about the Freyd conjecture

Developing Leadership in a National Cohort of Secondary Biology Teachers: Uses of an On-Line Course Structure to Develop Geographically Distant Professional Learning Community

This report is a descriptive study of the role that on-line courses might have on the development of Professional Learning Communities (PLC’s) that support national leadership initiatives of participating high school biology teachers. The one hundred teachers involved in the Life Sciences for a Global Community (LSGC) Institute are expected not only to deepen their content knowledge, but also impact their district and state biology curricula. Additionally, the dispersion of Institute participants across the country presents a unique opportunity to develop, communicate. and implement a national coherent reform agenda. However, the geographic distance presents a barrier to collaborative design of leadership projects. Therefore, the LSGC Institute designed web-based, distance learning courses as a means for both the instruction and development of distant professional relationships

New results on multidimensional Chinese remainder theorem

The Chinese remainder theorem (CRT) [McClellan and Rader 1979] has been well known for applications in fast DFT computations and computer arithmetic. Guessoum and Mersereau [1986] first made headway in extending the CRT to multidimensional (MD) nonseparable systems and showing its usefulness. The present letter generalize the result and present a more general form. This more general MDCRT is an exact counterpart of 1DCRT