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title = "Fractional Order Transfer Functions"
author = ["Thomas Dehaeze"]
author = ["Dehaeze Thomas"]
draft = false
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Tags
:
: [Digital Filters]({{< relref "digital_filters.md" >}})
## Example Using the FOMCON toolbox {#example-using-the-fomcon-toolbox}
@@ -21,7 +21,7 @@ Here are the parameters that are used to define the wanted properties of the fra
r = 0.5; % Wanted slope, The corresponding phase will be pi*r
```
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:
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:
```matlab
G = oustafod(r,n,wb,wh);
@@ -37,8 +37,14 @@ G =
Continuous-time transfer function.
```
Few examples of different slopes are shown in Figure [1](#org9241d6d).
Few examples of different slopes are shown in Figure [1](#figure--fig:approximate-deriv-int).
<a id="org9241d6d"></a>
<a id="figure--fig:approximate-deriv-int"></a>
{{< figure src="/ox-hugo/approximate_deriv_int.png" caption="Figure 1: Example of fractional approximations" >}}
{{< figure src="/ox-hugo/approximate_deriv_int.png" caption="<span class=\"figure-number\">Figure 1: </span>Example of fractional approximations" >}}
## Bibliography {#bibliography}
<style>.csl-entry{text-indent: -1.5em; margin-left: 1.5em;}</style><div class="csl-bib-body">
</div>