Discrete Hartley Transform - Definition

Definition

Formally, the discrete Hartley transform is a linear, invertible function H : Rn -> Rn (where R denotes the set of real numbers). The N real numbers x0, ...., xN-1 are transformed into the N real numbers H0, ..., HN-1 according to the formula

H_k = \sum_{n=0}^{N-1} x_n \left \quad \quad k = 0, \dots, N-1 .

The combination is sometimes denoted, and should be contrasted with the that appears in the DFT definition (where i is the imaginary unit).

As with the DFT, the overall scale factor in front of the transform and the sign of the sine term are a matter of convention. Although these conventions occasionally vary between authors, they do not affect the essential properties of the transform.

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