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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 ...
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4 votes
1 answer
59 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 ...
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6 votes
2 answers
172 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 ...
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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 ...
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2 votes
0 answers
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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), ...
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  • 121
0 votes
1 answer
148 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-...
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2 votes
2 answers
205 views

How exactly does one apply a Hanning Window for a spectral estimate?

PREAMBLE I am a graduate student researching evolutionary ecology. My supervisor and I have been trying to learn how to simulate colored noise, discretely, by the $\frac{1}{f^\alpha}$ power law for $\...
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1 vote
2 answers
169 views

Why is "$1/\mathrm{Hz}$" unchanged while converting$\mathrm{V}^2/\mathrm{Hz}$ to $\mathrm{dB}/\mathrm{Hz}$?

When computing power spectral density via Fourier transform and Parseval's theorem, one gets units of $V^2/Hz$ (e.g. Wiki). As a popular next step, the following unit conversion is widely used: $V^2/...
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1 vote
0 answers
39 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, ...
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2 votes
1 answer
14k 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 ...
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2 votes
0 answers
158 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?
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