An Integral Transform which shares some features with the Fourier Transform, but which (in the discrete
case), multiplies the Kernel by
(1) |
(2) |
The discrete version of the Hartley transform can be written explicitly as
(3) | |||
(4) |
(5) |
(6) | |||
(7) | |||
(8) |
(9) | |||
(10) |
(11) |
(12) | |||
(13) |
The Discrete Fourier Transform
(14) |
(15) | |||
(16) |
(17) |
See also Discrete Fourier Transform, Fast Fourier Transform, Fourier Transform
References
Arndt, J. ``The Hartley Transform (HT).'' Ch. 2 in ``Remarks on FFT Algorithms.''
http://www.jjj.de/fxt/.
Bracewell, R. N. The Fourier Transform and Its Applications. New York: McGraw-Hill, 1965.
Bracewell, R. N. The Hartley Transform. New York: Oxford University Press, 1986.
© 1996-9 Eric W. Weisstein