Recent Advances in Fourier Analysis and Its Applications

1. Front Matter

   Pages i-x

   PDF

2. Chemical, Physical and Biomedical Applications

   1. Front Matter

      Pages 1-1

      PDF

   2. A Minimal Principle in the Direct Methods of X-Ray Crystallography

      • Herbert Hauptman

      Pages 3-15

   3. Fourier Shape Analysis Of Anatomic Structures

      • D. N. Kennedy, P. A. Filipek, V. S. Caviness

      Pages 17-28

   4. Harmonic Analysis of the Semi-Classical Limit

      • Ketill Ingolfsson

      Pages 29-40

   5. Fourier Transform in Non-Euclidean Space and its Applications to Physics

      • M. Kovalyov, M. Legare

      Pages 41-57

   6. Complex Finite Fourier Transform Techniques Applied to Thermal Energy Storage Problems

      • Mazhar Ünsal

      Pages 59-72

   7. Spline Interpolation of Data of Power Growth

      • A. Jakimovski

      Pages 73-75

3. Polynomials with Restricted Coefficients

   1. Front Matter

      Pages 77-77

      PDF

   2. Properties on the Unit Circle of Polynomials with Unimodular Coefficients

      • Donald J. Newman, André Giroux

      Pages 79-81

   3. On the Maximum Modulus for a Certain Class of Unimodular Trigonometric Polynomials

      • George Benke

      Pages 83-100

   4. Number Theory and Fourier Analysis Applications in Physics, Acoustics and Computer Science

      • M. R. Schroeder

      Pages 101-129

   5. Functions of Modulus 1 on Z _n Whose Fourier Transforms Have Constant Modulus, and “CYCLIC n-ROOTS”

      • Göran Björck

      Pages 131-140

4. Fourier Analysis in Engineering

   1. Front Matter

      Pages 141-141

      PDF

   2. Uncertainty Principle Inequalities and Spectrum Estimation

      • John J. Benedetto

      Pages 143-182

   3. The Generalized Pencil-Of-Function (GPOF) Method for Extracting Poles from Transient Responses

      • Yingbo Hua, Tapan K. Sarkar, Fengdo Hu

      Pages 183-199

   4. Application of Conjugate Gradient Method and FFT to Electromagnetics and Signal Processing Problems

      • Saila Ponnapalli, Tapan K. Sarkar, Ercument Arvas

      Pages 201-220

   5. On the Application of Fourier Transformation in Antenna Measurements

      • K. Van’T Klooster

      Pages 221-236

   6. Computations in X-Ray Crystallography

      • Richard Tolimieri, Myoung An

      Pages 237-250

   7. A New Approach to Irregular Sampling of Band-Limited Functions

      • Karlheinz Gröchenig

      Pages 251-260

This volume contains papers presented at the July, 1989 NATO Advanced Study Institute on Fourier Analysis and its Applications. The conference, held at the beautiful II Ciocco resort near Lucca, in the glorious Tuscany region of northern Italy, created a dynamic in­ teraction between world-renowned scientists working in the usually disparate communities of pure and applied Fourier analysts. The papers to be found herein include important new results in x-ray crystallography by Nobel Laureate Herbert Hauptman, the application of the new concept of bispectrum to system identification by renowned probabilist Athanasios Papoulis, fascinating appli­ cations of number theory in Fourier analysis by eminent electrical engineer Manfred R. Schroeder, and exciting concepts regarding polynomials with restricted coefficients by foremost mathematical problem solver Donald J. Newman. The remaining papers further illustrate the inherent power and beauty of classical Fourier analysis, whether the results presented were sought as an end in themselves, or whether these classical methods were employed as a tool in illustrating and solving a particular applied problem. From antenna design to concert hall acoustics to image and speech processing to unimodular polynomi­ als, each conference participant benefited significantly from his or her exposure, in many cases for the first time, to those scientists on the other end of the spectrum from them­ selves. The purpose of this volume is to pass those benefits on to the reader.

• Fourier analysis
• Fourier transform
• acoustics
• coding
• crystallography
• distribution
• fast Fourier transform
• fast Fourier transform (FFT)
• harmonic analysis
• signal processing
• system identification
• uncertainty

• Prometheus Inc., Newport, USA

  J. S. Byrnes

• University of Massachusetts at Boston, Boston, USA

  J. S. Byrnes

• Harvard University, Cambridge, USA

  Jennifer L. Byrnes

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