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In 1942, Ralph Hartley proposed an analogue of the Fourier transform in his article "A More Symmetrical Fourier Analysis Applied to Transmission Problems".
Just like Fourier transform (FT), Hartley transform (HT) turns the original signal into a sum of trigonometric functions. But there is one significant difference between them. FT converts real values to complex numbers, while HT provides only real results. Because of this difference, the Hartley transform did not become popular - scientists and technicians did not see any advantages in it and continued to use the usual Fourier transform. In 1983, Ronald Bracewell presented a discrete version of the Hartley transform.

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