... Filters1
Adapted from arXiv.org publication arXiv:1606.06154 [cs.CE].
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....2
In engineering, it is more common to use the unilateral Laplace transform, in which the integral traverses $ [0,\infty)$ , and the differentiation theorem becomes $ {\cal L}_s\{x^{(1)}\} = s\,X(s)-x(0)$ .
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... parts.3
https://ccrma.stanford.edu/~jos/filters/Differentiation.html
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...,4
A function of time $ f(t)$ is said to be causal if $ f(t)=0$ for all $ t<0$ .
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... formula.5
https://en.wikipedia.org/wiki/Cauchy_formula_for_repeated_integration
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... function6
https://en.wikipedia.org/wiki/Gamma_function
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... differintegral,7
https://en.wikipedia.org/wiki/Differintegral
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....8
Our definition of $ \alpha$ is the negative of its usual definition in fractional calculus. We keep it so that $ \alpha$ can refer to the slope of the Bode magnitude plot, instead of the negative slope. Note also that we allow $ \alpha>0$ , but only consider $ \alpha\in\mathbb{R}$ .
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... calculus9
http://nrich.maths.org/1369
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... MATLAB,10
https://www.mathworks.com/
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... distribution.11
http://www.gnu.org/software/octave/
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...VossAndClarke78.12
http://123.physics.ucdavis.edu/week_3_files/voss-clarke.pdf
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... Web13
https://ccrma.stanford.edu/~jos/sasp/Example_Synthesis_1_F_Noise.html
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... distribution.14
faust.grame.fr
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... rates.15
http://www.firstpr.com.au/dsp/pink-noise/
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... log-frequency.16
https://en.wikipedia.org/wiki/Bode_plot
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... behavior.17
https://en.wikipedia.org/wiki/Phase_margin
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