Editing Hartley transform (section)

{{short description|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,<ref name="Hartley_1942"/> and is one of many known [[Fourier-related transform]]s. Compared to the Fourier transform, the Hartley transform has the advantages of transforming [[real number|real]] functions to real functions (as opposed to requiring [[complex number]]s) 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.<ref name="Bracewell_1983"/>

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.<ref name="Villasenor_1994"/> However, optical Hartley transforms<!-- apparently NOT abbreviated as OHT, as OHT used for something else --> do not seem to have seen widespread use.