A Unified Approach to Fast Algorithms of Discrete Trigonometric Transforms
ROSTOCK UNIV (GERMANY) DEPT OF MATHEMATICS
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We present a unified approach to fast algorithms of various discrete trigonometric transforms. With the help of so-called Euler formulas we describe an elegant and useful connection between Fourier matrices and trigonometric matrices. It is known that FFTs are closely related to the factorizations of the unitary Fourier matrix into a product of unitary sparse matrices. Using these Euler formulas and FFTs, we obtain fast algorithms of discrete trigonometric transforms. As a further consequence of these Euler formulas and Gaussian sums we compute all eigenvalues of some trigonometric matrices.
- Numerical Mathematics
- Theoretical Mathematics