F or many tasks involving Fourier analysis, a spreadsheet is an excellent tool. Using examples, this article shows that for data sets involving perhaps a hundred points and a few tens of coefficients, a spreadshe& method is practical and quick on perwnal computers such as the Macintosh SE or the IBM PC AT and compatibles. With enhanced hardware such as floating-point co-pmcaasor chips, the numb...

We study several functional properties of isometric and almost isometric unconditionality and state them as a property of families of multipliers. The most general such notion is that of “metric unconditional approximation property”. We characterize this “(umap)” by a simple property of “block unconditionality” for spaces with nontrivial cotype. We focus on subspaces of Banach spaces of functio...

In the solution of Fluid-Structure Interaction problems, partitioned procedures are modular algorithms that involve separate fluid and structure solvers, that interact, in an iterative framework, through the exchange of suitable transmission conditions at the FS interface. In this work we study, using Fourier analysis, the convergence of partitioned algorithms based on Robin transmission condit...

(Oil) and (lll)B. This observation is consistent with the work of Coldren et a/. on the sensitivity of the etch rate of InP in HC1 to the crystal orientation. The profile in Fig. 2 was obtained using a mixture of 1(HC1): 3(H3POJ (again the grating orientation is (Oil)), In this case the profile is rectangular with a depth of c*2000 A. Here, the etched depth is not limited by the formation of in...

1.1. Stirling’s formula. Laplace’s approach to Stirling’s formula is noteworthy first, because it makes a direct connection with the Gaussian (normal) distribution (whereas in other approaches the Gaussian distribution enters indirectly, or not at all), and second, because it provides a general strategy for the asymptotic approximation of a large class of integrals with a large parameter. Stirl...

This paper focusses on some of the more dif-cult issues involved in creating an automatic transcription system. The initial stages of the project follow traditional approaches based on Fourier analysis, but as these methods are not suuciently robust to process arbitrary musical data correctly, they are augmented by models of auditory perception derived from auditory scene analysis and dynamic m...

Fourier spectrum of the boundary values of functions in the complex Hardy Space H(C+) is characterized for p ∈ (0, 2). First, functions f in the L(R) can be decomposed into a sum g + h, where g and h are the non-tangential boundary limits of function in H(C+) and H(C−) in the sense of L(R), where H(C+) and H(C−) are the Hardy spaces in the upper and lower complex plane C+ and C−, respectively. ...

The Fourier spectra of circular gratings having sine or cosine radial profiles are derived, and their particular properties are discussed. These results are then extended to the most general form of circular sinusoidal gratings, namely: circular sine or cosine gratings with any arbitrary radial phase. q 1998 Elsevier Science B.V.

If X is a closed subset of the real line, denote by GX the supremum of the size of the gap in the Fourier spectrum, taken over all non-trivial finite complex measures supported on X. In this paper we attempt to find GX in terms of metric properties of X.

Whenever ranking data are collected, such as in elections, surveys, and database searches, it is frequently the case that partial rankings are available instead of, or sometimes in addition to, full rankings. Statistical methods for partial rankings have been discussed in the literature. However, there has been relatively little published on their Fourier analysis, perhaps because the abstract ...