Hartley transform

Summary

The Hartley transform is an integral transform like the Fourier transform, but with the real kernel $\cos(\omega t) + \sin(\omega t)$ in place of $e^{-i\omega t}$. It sends real functions to real functions, and with the symmetric normalization it is its own inverse. For a real function it carries the same information as the Fourier transform. For a real function $f$, the even part of the Hartley transform of $f$ is the real part of the Fourier transform of $f$. Its odd part is minus the imaginary part of the Fourier transform of $f$. Its discrete version is used as a real-arithmetic alternative to the discrete Fourier transform.