Hartley Transform - Properties

Properties

The Hartley transform is a real linear operator, and is symmetric (and Hermitian). From the symmetric and self-inverse properties, it follows that the transform is a unitary operator (indeed, orthogonal).

There is also an analogue of the convolution theorem for the Hartley transform. If two functions and have Hartley transforms and, respectively, then their convolution has the Hartley transform:

Z(\omega) = \{ \mathcal{H} (x * y) \} = \sqrt{2\pi} \left( X(\omega) \left + X(-\omega) \left \right) / 2

Similar to the Fourier transform, the Hartley transform of an even/odd function is even/odd, respectively.

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