Update Content - 2022-03-15
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title = "Fractional Order Transfer Functions"
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author = ["Thomas Dehaeze"]
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author = ["Dehaeze Thomas"]
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draft = false
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Tags
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:
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: [Digital Filters]({{< relref "digital_filters.md" >}})
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## Example Using the FOMCON toolbox {#example-using-the-fomcon-toolbox}
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r = 0.5; % Wanted slope, The corresponding phase will be pi*r
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```
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Then, to create an approximation of a fractional-order operator \\(s^r\\) of order \\(n\\) which is valid in the frequency range \\([\omega\_b\, \omega\_h]\\), the `oustafod` function can be used:
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Then, to create an approximation of a fractional-order operator \\(s^r\\) of order \\(n\\) which is valid in the frequency range \\([\omega\_b\\, \omega\_h]\\), the `oustafod` function can be used:
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```matlab
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G = oustafod(r,n,wb,wh);
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Continuous-time transfer function.
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```
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Few examples of different slopes are shown in Figure [1](#org9241d6d).
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Few examples of different slopes are shown in Figure [1](#figure--fig:approximate-deriv-int).
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<a id="org9241d6d"></a>
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<a id="figure--fig:approximate-deriv-int"></a>
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{{< figure src="/ox-hugo/approximate_deriv_int.png" caption="Figure 1: Example of fractional approximations" >}}
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{{< figure src="/ox-hugo/approximate_deriv_int.png" caption="<span class=\"figure-number\">Figure 1: </span>Example of fractional approximations" >}}
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## Bibliography {#bibliography}
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<style>.csl-entry{text-indent: -1.5em; margin-left: 1.5em;}</style><div class="csl-bib-body">
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</div>
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