Signal and System Approximation from General Measurements

In this paper we analyze the behavior of system approximation processes for stable linear time-invariant (LTI) systems and signals in the Paley-Wiener space PW_\pi^1. We consider approximation processes, where the input signal is not directly used to generate the system output, but instead a sequence of numbers is used that is generated from the input signal by measurement functionals. We consider classical sampling which corresponds to a pointwise evaluation of the signal, as well as several more general measurement functionals. We show that a stable system approximation is not possible for pointwise sampling, because there exist signals and systems such that the approximation process diverges. This remains true even with oversampling. However, if more general measurement functionals are considered, a stable approximation is possible if oversampling is used. Further, we show that without oversampling we have divergence for a large class of practically relevant measurement procedures.Comment: This paper will be published as part of the book "New Perspectives on Approximation and Sampling Theory - Festschrift in honor of Paul Butzer's 85th birthday" in the Applied and Numerical Harmonic Analysis Series, Birkhauser (Springer-Verlag). Parts of this work have been presented at the IEEE International Conference on Acoustics, Speech, and Signal Processing 2014 (ICASSP 2014

Josef Meixner: his life and his orthogonal polynomials

This paper starts with a biographical sketch of the life of Josef Meixner. Then his motivations to work on orthogonal polynomials and special functions are reviewed. Meixner's 1934 paper introducing the Meixner and Meixner-Pollaczek polynomials is discussed in detail. Truksa's forgotten 1931 paper, which already contains the Meixner polynomials, is mentioned. The paper ends with a survey of the reception of Meixner's 1934 paper.Comment: v4: 18 pages, generating function for Krawtchouk polynomials on p.10 correcte

Measures of fixed capital in agriculture

Capital is a fundamental component of agricultural production, and the accumulation of capital is key to growth in agriculture and the process of development. Unfortunately, cross-country data sets on agricultural fixed capital are rare. Using a common methodology that allows comparisons across countries, as well as over time, this paper introduces a data series on fixed capital in agriculture, based on national accounts data. The fixed capital measure differs remarkably from the Food and Agriculture Organization's data series on tractors, which has been widely utilized as a proxy for agricultural fixed capital. The authors construct comparable measures of capital in livestock and tree stock. They examine the evolution of the capital stocks from 1970 to 2000, paying particular attention to the changing composition of agricultural capital, as well as differences in the accumulation of capital for high-income and middle and lower-income countries. Using the capital measures in agricultural productivity analyses, the data yield estimated input elasticities substantially different from those found previously in the literature. The authors show explicitly that this is due to the improved data set on agricultural capital stocks, as well as the methodology used in the study.Economic Theory&Research,Investment and Investment Climate,Rural Development Knowledge&Information Systems,Economic Growth,Emerging Markets

Heterogeneous technology and panel data : the case of the agricultural production function

The paper presents empirical analysis of a panel of countries to estimate an agricultural production function using a measure of capital in agriculture absent from most studies. The authors employ a heterogeneous technology framework where implemented technology is chosen jointly with inputs to interpret information obtained in the empirical analysis of panel data. The paper discusses the scope for replacing country and time effects by observed variables and the limitations of instrumental variables. The empirical results differ from those reported in the literature for cross-country studies, largely in augmenting the role of capital, in combination with productivity gains, as a driver of agricultural growth. The results indicate that total factor productivity increased at an average rate of 3.2 percent, accounting for 59 percent of overall growth. Most of the remaining gains stem from large inflows of fixed capital into agriculture. The results also suggest possible constraints to fertilizer use.Economic Theory&Research,Labor Policies,Economic Growth,E-Business,Rural Development Knowledge&Information Systems

A new database on investment and capital for agriculture and manufacturing

In this paper, the authors document a new database on sectoral investment and capital, providing details about sources of investment data and the method used to convert those data series into capital stock series. They also provide a copy of the computer program used to implement the method. The data set is available for electronic distribution and will soon be posted on the World Wide Web. They broadly define agricultural capital and calculate series for fixed capital as well as capital embodied in livestock and treestock.Agricultural Research,Banking Law,Economic Theory&Research,International Terrorism&Counterterrorism,Fiscal&Monetary Policy,Economic Theory&Research,Agricultural Research,International Terrorism&Counterterrorism,National Governance,ICT Policy and Strategies