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:

    “... we all know the wag’s definition of a philanthropist: a man whose charity increases directly as the square of the distance.”
    —George Eliot [Mary Ann (or Marian)

    “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)

    “Beauty, like all other qualities presented to human experience, is relative; and the definition of it becomes unmeaning and useless in proportion to its abstractness. To define beauty not in the most abstract, but in the most concrete terms possible, not to find a universal formula for it, but the formula which expresses most adequately this or that special manifestation of it, is the aim of the true student of aesthetics.”
    —Walter Pater (1839–1894)