Shifted Fourier matrices and their tridiagonal commutors

SIAM Journal on Matrix Analysis and Applications

Volumn 24, Issue 3, 2003, Pages 809-821

  Clary, Stuart ^a   Mugler, Dale H ^a  

^a UNIVERSITY OF AKRON   (United States)

Author keywords

Centered Fourier matrix; Extended tridiagonal matrix; Generalized Fourier matrix; Shifted Fourier matrix; Tridiagonal commutor

Indexed keywords

EID: 0042415176     PISSN: 08954798     EISSN: None     Source Type: Journal    
DOI: 10.1137/S0895479800372754     Document Type: Article

References (17)

1. D. H. BAILEY AND P. N. SWARZTRAUBER, The fractional Fourier transform and applications, SIAM Rev., 33 (1991), pp. 389-404.
2. G. BONGIOVANNI, P. CORSINI, AND G. FROSINI, One-dimensional and two-dimensional generalized discrete Fourier transforms, IEEE Trans. Acoust. Speech Signal Process., ASSP-24 (1976), pp. 97-99.
3. G. BONNEROT AND M. BELLANGER, Odd-time odd-frequency discrete Fourier transform for symmetric real-valued series, Proc. IEEE, 64 (1976), pp. 392-393.
4. B. W. DICKINSON AND K. STEIGLITZ, Eigenvectors and functions of the discrete Fourier transform, IEEE Trans. Acoust. Speech Signal Process., ASSP-30 (1982), pp. 25-31.
5. R. L. GRAHAM, D. E. KNUTH, AND O. PATASHNIK, Concrete Mathematics: A Foundation for Computer Science, 2nd ed., Addison-Wesley, Reading, MA, 1994.
6. F. A. GRÜNBAUM, Eigenvectors of a Toeplitz matrix: Discrete version of the prolate spheroidal wave functions, SIAM J. Algebraic Discrete Methods, 2 (1981), pp. 136-141.
7. F. A. GRÜNBAUM, Toeplitz matrices commuting with tridiagonal matrices, Linear Algebra Appl., 40 (1981), pp. 25-36.
8. F. A. GRÜNBAUM, The eigenvectors of the discrete Fourier transform: A version of the Hermite functions, J. Math. Anal. Appl., 88 (1982), pp. 355-363.
9. F. A. GRÜNBAUM, A remark on Hilbert's matrix, Linear Algebra Appl., 43 (1982), pp. 119-124.
10. S. A. MARTUCCI, Symmetric convolution and the discrete sine and cosine transforms, IEEE Trans. Signal Process., 42 (1994), pp. 1038-1051.
11. D. H. MUGLER AND S. CLARY, Discrete Hermite functions, in Proceedings of the International Conference on Scientific Computing and Mathematical Modeling, Milwaukee, WI, 2000, pp. 318-321.
12. D. H. MUGLER AND S. CLARY, Discrete Hermite functions and the fractional Fourier transform, in Proceedings of the International Conference on Sampling Theory and Applications, Orlando, FL, 2001, pp. 303-308.
13. H. M. OZAKTAS, Z. ZALEVSKY, AND M. A. KUTAY, The Fractional Fourier Transform with Applications in Optics and Signal Processing, John Wiley and Sons, New York, 2001.
14. K. R. RAO AND P. YIP, Discrete Cosine Transform: Algorithms, Advantages, Applications, Academic Press, New York, 1990.
15. R. O. ROWLANDS, The odd discrete Fourier transform, in Conference Record of the IEEE International Conference on Acoustics, Speech, and Signal Processing, Philadelphia, PA, 1976, pp. 130-133.
16. W. W. SAWYER, On the matrix with elements 1/(r + s - 1), Canad. Math. Bull., 17 (1974), pp. 297-298.
17. G. STRANG, The discrete cosine transform, SIAM Rev., 41 (1999), pp. 135-147.