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Resolution properties of the Fourier method for discontinuous waves
- Publication Year :
- 1992
- Publisher :
- United States: NASA Center for Aerospace Information (CASI), 1992.
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Abstract
- In this paper we discuss the wave-resolution properties of the Fourier approximations of a wave function with discontinuities. It is well known that a minimum of two points per wave is needed to resolve a periodic wave function using Fourier expansions. For Chebyshev approximations of a wave function, a minimum of pi points per wave is needed. Here we obtain an estimate for the minimum number of points per wave to resolve a discontinuous wave based on its Fourier coefficients. In our recent work on overcoming the Gibbs phenomenon, we have shown that the Fourier coefficients of a discontinuous function contain enough information to reconstruct with exponential accuracy the coefficient of a rapidly converging Gegenbauer expansion. We therefore study the resolution properties of a Gegenbauer expansion where both the number of terms and the order increase.
- Subjects :
- Numerical Analysis
Subjects
Details
- Language :
- English
- Database :
- NASA Technical Reports
- Notes :
- AF-AFOSR-90-0093, , NAG1-1145, , N00014-91-J-4016, , NAS1-18605, , DAAL03-91-G-0123, , RTOP 505-90-52-01
- Publication Type :
- Report
- Accession number :
- edsnas.19920021472
- Document Type :
- Report