Editing Pink noise (section)

=== Power-law spectra ===
The power spectrum of pink noise is <math>\frac{1}{f}</math> only for one-dimensional signals. For two-dimensional signals (e.g., images) the average power spectrum at any orientation falls as <math>\frac{1}{f^2}</math>, and in <math>d</math> dimensions, it falls as <math>\frac{1}{f^d}</math>. In every case, each octave carries an equal amount of noise power. 

The average amplitude <math>a_\theta</math> and power <math>p_\theta</math> of a pink noise signal at any orientation <math>\theta</math>, and the total power across all orientations, fall off as some power of the frequency. The following table lists these power-law frequency-dependencies for pink noise signal in different dimensions, and also for general power-law colored noise with power <math>\alpha</math> (e.g.: [[Brown noise]] has <math>\alpha=2</math>): <ref name="Das-thesis"/>

{| class="wikitable"
|+ Power-law spectra of pink noise
|-
! dimensions !! avg. amp. <math>a_\theta(f)</math> !! avg. power <math>p_\theta(f)</math> !! tot. power <math>p(f)</math>
|-
| 1 || <math>1/\sqrt{f}</math> || <math>1/f</math> || <math>1/f</math>
|-
| 2 || <math>1/f</math> || <math>1/f^2</math> || <math>1/f</math>
|-
| 3 || <math>1/f^{3/2}</math> || <math>1/f^3</math> || <math>1/f</math>
|-
| <math>d</math> || <math>1/f^{d/2}</math> || <math>1/f^d</math> || <math>1/f</math>
|-
| <math>d</math>, power <math>\alpha</math> || <math>1/f^{\alpha d /2}</math> || <math>1/f^{\alpha d}</math> || <math>1/f^{1+(\alpha-1)d}</math>
|}