“Hartley Transform”的概念、定义、习题解题方法及翻译-数学辞典

单词

Hartley Transform

释义

Hartley Transform

An Integral Transform which shares some features with the Fourier Transform, but which (in the discretecase), multiplies the Kernel by

(1)

instead of

(2)

The Hartley transform produces Real output for a Real input, and is its owninverse. It therefore can have computational advantages over the Discrete Fourier Transform, although analyticexpressions are usually more complicated for the Hartley transform.

The discrete version of the Hartley transform can be written explicitly as

			(3)
			(4)

where

denotes the Fourier Transform. The Hartley transform obeys the Convolution property

(5)

where

			(6)
			(7)
			(8)

(Arndt). Like the Fast Fourier Transform, there is a ``fast'' version of the Hartley transform. A decimation intime algorithm makes use of

			(9)
			(10)

where

denotes the sequence with elements

(11)

A decimation in frequency algorithm makes use of

			(12)
			(13)

The Discrete Fourier Transform

(14)

can be written

			(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.

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