This book provides a meaningful resource for applied mathematics through Fourier analysis. It develops a unified theory of discrete and continuous (univariate) Fourier analysis, the fast Fourier transform, and a powerful elementary theory of generalized functions and shows how these mathematical ideas can be used to study sampling theory, PDEs, probability, diffraction, musical tones, and wavelets. The book contains an unusually complete presentation of the Fourier transform calculus. It uses concepts from calculus to present an elementary theory of generalized functions. FT calculus and generalized functions are then used to study the wave equation, diffusion equation, and diffraction equation. Real-world applications of Fourier analysis are described in the chapter on musical tones. A valuable reference on Fourier analysis for a variety of students and scientific professionals, including mathematicians, physicists, chemists, geologists, electrical engineers, mechanical engineers, and others.

Abstract. This paper presents a design-space exploration of an application-specific instruction-set processor (ASIP) for the computation of various cryptographic pairings over Barreto-Naehrig curves (BN curves). Cryptographic pairings are based on elliptic curves over finite fields-in the case of BN curves a field Fp of large prime order p. Efficient arithmetic in these fields is crucial for fast computation of pairings. Moreover, computation of cryptographic pairings is much more complex than elliptic-curve cryptography (ECC) in general. Therefore, we facilitate programming of the proposed ASIP by providing a C compiler.In order to speed up Fp arithmetic, a RISC core is extended with additional scalable functional units. Because the resulting speedup can be limited by the memory throughput, utilization of multiple data-memory banks is proposed.The presented design needs 15.8 ms for the computation of the Optimal-Ate pairing over a 256-bit BN curve at 338 MHz implemented with a 130 nm standard cell library. The processor core consumes 97 kGates making it suitable for the use in embedded systems.

In this paper, we present a method for identification of binary objects from a given set of radon projections. Given a suitably regular 2-D function f, we form a new function g from f by using the operations of reflection, scaling, translation, and rotation. We show how the radon projections of g are related to those of f and devise a procedure that can be used to determine the parameters from the radon projections of f and g. We illustrate this process using a family of block images that include common 7 x 5 pixel representations for the letters A, B,....., Z.

No abstract