# Is there $\frac{1}{f^{0.5}}$ noise?

I've heard of $\frac{1}{f^0}$ noise (white noise), $\frac{1}{f}$ (pink, or sometimes tan noise), and $\frac{1}{f^2}$ (brown noise). But why no $\frac{1}{f^{0.5}}$ or $\frac{1}{f^{\pi-2}}$ noise. Do these exist or are they just rounded of to pink noise. Also I read that the exponent must lie between 0 and 2 but whats wrong with $\frac{1}{f^3}$ noise?

EDIT: by exist I mean do they have waveforms that oscillate, whether or not we can hear them I find irrelevant.

• And what you mean by "exist" in this case? You can generate $1/f^3$ noise, but everything with exponent larger than 2 is named "black noise" and defined almost as a silence (with zero power density with a few random spikes allowed). Oct 19 '15 at 10:47
• @m0nhawk by exist I mean do the have waveforms the are oscillate, whether or not we can hear them I find irrelevant. Oct 26 '15 at 1:27
• Would Signal Processing or Cross Validated be a better home for this question? Oct 26 '15 at 8:52
• Sure, you can in principle have any frequency distribution you want. Whether or not any physical processes in the real world create noise with that spectrum is another question, but you can easily generate it on a computer. Aug 5 '17 at 0:57

• Actually, creating a digital filter with a given response is a major challenge, and it's not always possible to do it exactly. In particular, I think a $1/f$ (aka "3 dB/octave") filter is not possible. Of course you can approximate it with an FFT or by a clever combination of other filters, but there will always be deviations from the ideal response. Oct 26 '15 at 8:46
• Not in the sense I intended. A 6 dB/Octave filter ($1/f^2$), for example, can be implemented exactly using a simple IIR method. Oct 26 '15 at 9:41