Generalization To More Than One Dimension
The spectrum of pink noise is 1/f only for one-dimensional signals. For two-dimensional signals, e.g., images, the spectrum is reciprocal to f2. In general, in an n-dimensional system, the spectrum is reciprocal to fn. For higher-dimensional signals it is still true (by definition) that each octave carries an equal amount of noise power. The frequency spectrum of two-dimensional signals, for instance, is also two-dimensional, and the area covered by succeeding octaves is four times as large.
Read more about this topic: Pink Noise
Famous quotes containing the word dimension:
“Authority is the spiritual dimension of power because it depends upon faith in a system of meaning that decrees the necessity of the hierarchical order and so provides for the unity of imperative control.”
—Shoshana Zuboff (b. 1951)