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# Questions tagged [power-law]

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1answer
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### 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 ...
2answers
156 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 ...
0answers
36 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 ...
0answers
24 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 ...
0answers
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), ...
1answer
102 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-...
2answers
162 views

0answers
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, ...
1answer
13k views

### Conversion of transmitter power from Watts into dB

I've been practicing problems relating to the dB conversion and came across this interesting example problem. In the above example Tx power is defined in Watts and the conversion from the Watts to dB ...
0answers
156 views

### What is the image power law?

What exactly is the image power law mentioned at page 15 in here: Is it related to Gamma correction or the statistical power law Or anything to do with PSF of a camera?