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Resolution properties of the fourier method for discontinuous waves
| Content Provider | NASA Technical Reports Server (NTRS) |
|---|---|
| Author | Shu, Chi-Wang Gottlieb, David |
| Copyright Year | 1992 |
| Description | 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. |
| File Size | 633508 |
| Page Count | 22 |
| File Format | |
| Alternate Webpage(s) | http://archive.org/details/NASA_NTRS_Archive_19920021472 |
| Archival Resource Key | ark:/13960/t40s4pj4q |
| Language | English |
| Publisher Date | 1992-06-01 |
| Access Restriction | Open |
| Subject Keyword | Numerical Analysis Discontinuity Theorems Fourier Transformation Gibbs Phenomenon Periodic Functions Theorem Proving Chebyshev Approximation Fourier Analysis Wave Functions Fourier Series Resolution Ntrs Nasa Technical Reports Server (ntrs) Nasa Technical Reports Server Aerodynamics Aircraft Aerospace Engineering Aerospace Aeronautic Space Science |
| Content Type | Text |
| Resource Type | Technical Report |
