Integral transform closely related to the Fourier transform
In mathematics, the Hartley transform (HT) is an integral transform closely related to the Fourier transform (FT), but which transforms real-valued functions to real-valued functions. It was proposed as an alternative to the Fourier transform by Ralph V. L. Hartley in 1942,[1] and is one of many known Fourier-related transforms. Compared to the Fourier transform, the Hartley transform has the advantages of transforming real functions to real functions (as opposed to requiring complex numbers) and of being its own inverse.
The discrete version of the transform, the discrete Hartley transform (DHT), was introduced by Ronald N. Bracewell in 1983.[2]
The two-dimensional Hartley transform can be computed by an analog optical process similar to an optical Fourier transform (OFT), with the proposed advantage that only its amplitude and sign need to be determined rather than its complex phase.[3] However, optical Hartley transforms do not seem to have seen widespread use.
^Cite error: The named reference Hartley_1942 was invoked but never defined (see the help page).
^Cite error: The named reference Bracewell_1983 was invoked but never defined (see the help page).
^Cite error: The named reference Villasenor_1994 was invoked but never defined (see the help page).
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