# Questions tagged [power-law]

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### How to generate a power-law / pink noise signal?

Suppose I need to generate a time series where the intervals will be about 120 seconds every time, but with a small variation (e.g. 125, 130, 119, 118, 121, 129, etc) I want this variation not to be ...
42 views

### Does a power spectral density that follow a power law imply that the time hisory follows a power law?

This is a question related to this previous question "I cannot find reference (paper) of this relation $u(t)t^{α} ↔^{FT} f^{-(α+1)}$". The signal that I work with g(t), is the time history ...
165 views

### I cannot find reference (paper) of this relation $u(t)t^{α} ↔^{FT} f^{-(α+1)}$

I am struggling a lot in finding the reference (book or, even better, academic paper) that states that: $u(t)$ $t^{α} ↔^{FT} f^{-(α+1)}$ as I found here An Interesting Fourier Transform - 1/f ...
39 views

### Allan variance vs power spectrum density for noise estimation

I know than we can estimate noise level (and noise colors) from power spectrum density function OR from Allan variance. Why do we need Allan variance at all for such estimation? In my opinion PSD ...
26 views

### how to convert decay time to power law coefficiants

In audio, I am familiar with the definition of t-60, which is a characterization of a room impulse response (RIR) decay time. This characterization demands that the sound will have a 60 db decay over ...
47 views

### Relating Fourier and power-law descriptions of noise

I'm trying to understand this PDF, which is in English but has Polish authors, so there may be translation issues confusing me. The subject is the frequencies of sentence lengths in novels. Eq. (1), ...
129 views

### My Power Law (Gamma) Transformation Code Doesn't Compatible With Gamma Value

I'm trying to apply Power Law (Gamma) Transformation. Formula is simple: s = c*rγ. (c=1 , r= intensity , s= outputintensity). Here is detailed information: https://theailearner.com/2019/01/26/power-...
179 views

38 views

### Generating 3-dimension $1/f^\alpha$ noise

I'm stumped trying to find a way to generate a 3-dimensional $1/f^\alpha$ noise time series. Basically I want simulate a forcing that is $1/f^\alpha$ in the 2 space dimensions and $1/f^\beta$ in time, ...