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Plots upgedatet, hybirder Ansatz raus

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Patrick Hangl
2026-02-25 10:50:59 +01:00
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chapter_02.tex
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@@ -132,7 +132,6 @@ To reduce the required computing power, a hybrid static/adaptive filter design c
\caption{Hybrid adaptive filter design for noise reduction with a static part and an adaptive part.}
\label{fig:fig_anr_hybrid}
\end{figure}
\noindent Different approaches of the hybrid static/adaptive filter design will be evaluated and compared in regard of their required computing power in a later chapter of this thesis.
\subsection{Adaptive optimization strategies}
In the description of the concept of adaptive filtering above, the adaption of filter coefficients due to an error metric was mentioned but not further explained. The following subchapters shall cover the most important aspects of filter optimization in regard of adaptive noise reduction.
\subsubsection{Filter optimization and error metrics}
@@ -277,7 +276,7 @@ The following definitions of the involved signals shall help to better understan
\item Filter output / Cleaned signal: The output signal of the \ac{ANR} algorithm, representing the desired signal after noise reduction. This signal also equals the error signal of the adaptive filter.
\end{itemize}
The primary sensor receives the desired- and noise signal over their respective transfer functions and outputs the corrupted signal $d[n]$, which consists out of the recorded desired signal $s[n]$ and the corruption noise signal $n[n]$, whereas the noise signal sensor aims to receive (ideally) only the noise signal $v[n]$ over its transfer function and outputs the reference noise signal $x[n]$, which then feeds the adaptive filter.\\ \\
Additionally, now the relevant transfer functions of the overall system are illustrated in Figure \ref{fig:fig_anr_implant}. The transfer functions $C_n$, $D_n$, and $E_n$ describe the path from the signal sources to the cochlear implant system. As the sources, the relative location of the user to the sources and the medium between them can vary, these transfer functions are time-variant and unknown. After the signals reached the implant systems, we establish the possibility, that the remaining path of the signals is mainly depended on the sensitivity curve of the respective sensors and therefore can be seen as time-invariant and known. This known transfer functions, which are titled $A$ and $B$, allow us to apply a hybrid static/adaptive filter design for the \ac{ANR} implementation, as described in chapter 2.5.2.\\ \\
Additionally, now the relevant transfer functions of the overall system are illustrated in Figure \ref{fig:fig_anr_implant}. The transfer functions $C_n$, $D_n$, and $E_n$ describe the path from the signal sources to the cochlear implant system. As the sources, the relative location of the user to the sources and the medium between them can vary, these transfer functions are time-variant and unknown. After the signals reached the implant systems, we establish the possibility, that the remaining path of the signals is mainly depended on the sensitivity curve of the respective sensors and therefore can be seen as time-invariant and known.\\ \\
\begin{equation}
\label{equation_dn}
d[n] = s[n] + n[n] = t[n] * (C_nA) + v[n] * (D_nA)