Hartley Transform - Definition

Definition

The Hartley transform of a function f(t) is defined by:

H(\omega) = \left\{\mathcal{H}f\right\}(\omega) = \frac{1}{\sqrt{2\pi}}\int_{-\infty}^\infty f(t) \, \mbox{cas}(\omega t) \mathrm{d}t,

where can in applications be an angular frequency and

\mbox{cas}(t) = \cos(t) + \sin(t) = \sqrt{2} \sin (t+\pi /4) = \sqrt{2} \cos (t-\pi /4)\,

is the cosine-and-sine or Hartley kernel. In engineering terms, this transform takes a signal (function) from the time-domain to the Hartley spectral domain (frequency domain).

Read more about this topic:  Hartley Transform

Famous quotes containing the word definition:

    “The man who knows governments most completely is he who troubles himself least about a definition which shall give their essence. Enjoying an intimate acquaintance with all their particularities in turn, he would naturally regard an abstract conception in which these were unified as a thing more misleading than enlightening.”
    —William James (1842–1910)

    “The physicians say, they are not materialists; but they are:MSpirit is matter reduced to an extreme thinness: O so thin!—But the definition of spiritual should be, that which is its own evidence. What notions do they attach to love! what to religion! One would not willingly pronounce these words in their hearing, and give them the occasion to profane them.”
    —Ralph Waldo Emerson (1803–1882)

    “I’m beginning to think that the proper definition of “Man” is “an animal that writes letters.””
    —Lewis Carroll [Charles Lutwidge Dodgson] (1832–1898)