2.2
This commit is contained in:
Patrick Hangl
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@@ -49,12 +49,32 @@ During the description of transfer functions, the term ''filter'' was used but n
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\label{fig:fig_lowpass}
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\end{figure}
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Examples for an adaptive filter is the Least-Mean-Square-Algorithm used for adaptive noise reduction, which will be introduced in the following chapters.
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\subsection{Finite Impulse Response- and Infinite Impulse Response-filters}
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\subsection{Filter designs}
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Before we continue with the introduction to the actual topic of this thesis, ANR, two very essential filter designs need further explanation - the Finite Impulse Response- (FIR) and Infinite Impulse Response-filters (IIR).
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\subsubsection{Finite Impulse Response-filters}
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A Finite Impulse Respone Filter, commonly referred to as a ''Feedforward Filter'' is defined through the property, that it uses only present and past input values and not feedback from output samples - therefore the response of a FIR-filter reaches zero after a finite number of samples. Due to the fact, that there is no feedback, a FIR-filter offers unconditional stability, meaning that the filter response can´t diverge in any case. A disatavante to the FIR-filter desgin is the relatively slow frequency reaction compared to its IIR counterpart.
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A Finite Impulse Respone filter, commonly referred to as a ''Feedforward Filter'' is defined through the property, that it uses only present and past input values and not feedback from output samples - therefore the response of a FIR-filter reaches zero after a finite number of samples. Due to the fact, that there is no feedback, a FIR-filter offers unconditional stability, meaning that the filter response converges, no matter how the coefficients are set. A disadvantage to the FIR-desgin is the relatively slow frequency response compared to its IIR counterpart.
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\begin{equation}
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\label{equation_fir}
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y[n] = \sum_{k=1}^{M} b_kx[n-k]
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\end{equation}
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\begin{figure}[H]
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\centering
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\includegraphics[width=0.8\linewidth]{Bilder/fig_fir.jpg}
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\caption{FIR-filter}
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\label{fig:fig_fir}
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\end{figure}
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\subsubsection{Infinite Impulse Response-filters}
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A Ininite Impulse Respone Filter, commonly referred to as a ''Feedback Filter'' does, in contrary to its FIR-counterpart, use past output samples in addition to current and past input samples - hterefore the response of a IIR-filter theoretically continues indefinitely.
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A Ininite Impulse Respone filter, commonly referred to as a ''Feedback Filter'' does, in contrary to its FIR-counterpart, use past output samples in addition to current and past input samples - therefore the response of an IIR-filter theoretically continues indefinitely. This recursive nature allows IIR filter to achieve a sharp frequency response with significantly fewer coefficients than an equivalent FIR filter but it also opens up the possibility, that the filter-response diverges, depending on the set coefficients.
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\begin{equation}
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\label{equation_iir}
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y[n] = \sum_{k=1}^{M} b_kx[n-k] - \sum_{k=1}^{N} a_ky[n-k]
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\end{equation}
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\begin{figure}[H]
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\centering
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\includegraphics[width=0.8\linewidth]{Bilder/fig_iir.jpg}
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\caption{IIR-filter}
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\label{fig:fig_iir}
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\end{figure}
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\subsection{Introduction to Adaptive Nose Reduction}
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<mxCell id="5J26uNCy_atFF0Sp8wAd-3" value="" style="endArrow=classic;html=1;rounded=0;exitX=1;exitY=0.5;exitDx=0;exitDy=0;entryX=0.5;entryY=1;entryDx=0;entryDy=0;strokeWidth=2;" parent="1" source="OiLAJHeFUBjgwUQ8hIGB-2" target="OiLAJHeFUBjgwUQ8hIGB-4" edge="1">
|
||||
<mxGeometry width="50" height="50" relative="1" as="geometry">
|
||||
<mxPoint x="310" y="410" as="sourcePoint" />
|
||||
<mxPoint x="360" y="360" as="targetPoint" />
|
||||
@@ -66,13 +55,32 @@
|
||||
</Array>
|
||||
</mxGeometry>
|
||||
</mxCell>
|
||||
<mxCell id="5J26uNCy_atFF0Sp8wAd-8" value="b<sub>-1</sub>" style="edgeLabel;html=1;align=center;verticalAlign=bottom;resizable=0;points=[];labelPosition=center;verticalLabelPosition=top;fontSize=18;" vertex="1" connectable="0" parent="5J26uNCy_atFF0Sp8wAd-3">
|
||||
<mxGeometry x="-0.675" y="-5" relative="1" as="geometry">
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||||
<mxPoint x="-34" y="-45" as="offset" />
|
||||
<mxCell id="OiLAJHeFUBjgwUQ8hIGB-13" value="<font style="font-size: 20px;">Σ</font>" style="text;html=1;align=center;verticalAlign=middle;resizable=0;points=[];autosize=1;strokeColor=none;fillColor=none;" parent="1" vertex="1">
|
||||
<mxGeometry x="360" y="260" width="40" height="40" as="geometry" />
|
||||
</mxCell>
|
||||
<mxCell id="dvOqxy1bSSOmIYa8ABIz-1" value="<span style="font-size: 20px;">x[n]</span>" style="text;html=1;align=center;verticalAlign=middle;resizable=0;points=[];autosize=1;strokeColor=none;fillColor=none;" vertex="1" parent="1">
|
||||
<mxGeometry x="50" y="260" width="60" height="40" as="geometry" />
|
||||
</mxCell>
|
||||
<mxCell id="dvOqxy1bSSOmIYa8ABIz-3" value="<font style="font-size: 20px;">b<sub>1</sub></font>" style="text;html=1;align=center;verticalAlign=middle;resizable=0;points=[];autosize=1;strokeColor=none;fillColor=none;" vertex="1" parent="1">
|
||||
<mxGeometry x="185" y="260" width="40" height="40" as="geometry" />
|
||||
</mxCell>
|
||||
<mxCell id="dvOqxy1bSSOmIYa8ABIz-4" value="<font style=""><span style="font-size: 20px;">a<sub>1</sub></span></font>" style="text;html=1;align=center;verticalAlign=middle;resizable=0;points=[];autosize=1;strokeColor=none;fillColor=none;" vertex="1" parent="1">
|
||||
<mxGeometry x="500" y="420" width="40" height="40" as="geometry" />
|
||||
</mxCell>
|
||||
<mxCell id="dvOqxy1bSSOmIYa8ABIz-6" value="" style="endArrow=classic;html=1;rounded=0;entryX=-0.05;entryY=0.475;entryDx=0;entryDy=0;entryPerimeter=0;strokeWidth=2;" edge="1" parent="1" target="dvOqxy1bSSOmIYa8ABIz-3">
|
||||
<mxGeometry width="50" height="50" relative="1" as="geometry">
|
||||
<mxPoint x="110" y="280" as="sourcePoint" />
|
||||
<mxPoint x="155" y="230" as="targetPoint" />
|
||||
</mxGeometry>
|
||||
</mxCell>
|
||||
<mxCell id="OiLAJHeFUBjgwUQ8hIGB-13" value="<font style="font-size: 30px;">Σ</font>" style="text;html=1;align=center;verticalAlign=middle;resizable=0;points=[];autosize=1;strokeColor=none;fillColor=none;" parent="1" vertex="1">
|
||||
<mxGeometry x="360" y="255" width="40" height="50" as="geometry" />
|
||||
<mxCell id="dvOqxy1bSSOmIYa8ABIz-7" value="<span style="font-size: 20px;">x[n]*b<sub>1</sub></span>" style="text;html=1;align=center;verticalAlign=middle;resizable=0;points=[];autosize=1;strokeColor=none;fillColor=none;" vertex="1" parent="1">
|
||||
<mxGeometry x="250" y="240" width="80" height="40" as="geometry" />
|
||||
</mxCell>
|
||||
<mxCell id="dvOqxy1bSSOmIYa8ABIz-9" value="<span style="font-size: 20px;">x[n-1]*a<sub>1</sub></span>" style="text;html=1;align=center;verticalAlign=middle;resizable=0;points=[];autosize=1;strokeColor=none;fillColor=none;" vertex="1" parent="1">
|
||||
<mxGeometry x="380" y="400" width="100" height="40" as="geometry" />
|
||||
</mxCell>
|
||||
<mxCell id="dvOqxy1bSSOmIYa8ABIz-10" value="<span style="font-size: 20px;">y[n]</span>" style="text;html=1;align=center;verticalAlign=middle;resizable=0;points=[];autosize=1;strokeColor=none;fillColor=none;" vertex="1" parent="1">
|
||||
<mxGeometry x="700" y="260" width="60" height="40" as="geometry" />
|
||||
</mxCell>
|
||||
</root>
|
||||
</mxGraphModel>
|
||||
|
||||
Reference in New Issue
Block a user