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.

Read more about this topic:  Discrete Hartley Transform

Famous quotes containing the word definition:

    “According to our social pyramid, all men who feel displaced racially, culturally, and/or because of economic hardships will turn on those whom they feel they can order and humiliate, usually women, children, and animals—just as they have been ordered and humiliated by those privileged few who are in power. However, this definition does not explain why there are privileged men who behave this way toward women.”
    —Ana Castillo (b. 1953)

    “Although there is no universal agreement as to a definition of life, its biological manifestations are generally considered to be organization, metabolism, growth, irritability, adaptation, and reproduction.”
    —The Columbia Encyclopedia, Fifth Edition, the first sentence of the article on “life” (based on wording in the First Edition, 1935)