High-Level Plots neu

chapter_03.tex

@@ -119,7 +119,7 @@ After the general functionality of the \ac{ANR} algorithm has been verified with
 \noindent The error signal in Figure \ref{fig:fig_plot_2_wav.png} confirms the function of the algorithm and shows maxima corresponding to the maxima in the breathing noise, indicating the moments, when the \ac{ANR} algorithm is setting its coefficients again to adapt to the changing noise characteristics. It makes sense, that the adaption of the filter coefficients causes repeating maxima in the error signal, as the noise signal now is not static or periodic, but rather dynamic and changing it frequency and amplitude over time. The \ac{SNR}-Gain of 6.51 dB also indicates a significant improvement in signal quality and can be compared againtst the complex use case in the next subchapter, where the same audio tracks are used, but now with different transfer functions applied to them.
 \subsection{Complex ANR use case}
 To close the topic of high-level simulations of the \ac{ANR} algorithm, a more complex and realistic use case is finally introduced. In this scenario, the same two audio tracks of the previous use case are used - but now they pass different transfer functions. Now, an analytical solution is not possible anymore, as the transfer functions affect the signals in different ways, making it impossible to simply subtract the noise signal from the corrupted signal. This scenario represents a more realistic application of the \ac{ANR} algorithm, as it involves complex audio signals with varying frequency components and dynamics, as well as different transfer functions affecting the signals.\\ \\
-Therefore, the audio tracks from the previous example are now convolved with different transfer functions, which mimic the case, that the sensor recording the corrupted signal, shows another frequency response characteristic as the one recording the reference noise signal. This means, that the reference noise signal is now different to the noise signal corrupting the desired signal, making adaptive noise reduction the only feasible approach to reduce the noise from the corrupted signal.
+Therefore, the audio tracks from the previous example are now convolved with different transfer functions, which mimic the case, that the sensor recording the corrupted signal, shows another frequency response characteristic as the one recording the reference noise signal. Additionaly, a delay of 2 ms between the two signals is introduced, mimicing different loactions of the sensors and different preprocessing of the signals. This means, that the reference noise signal is now not only differs from the noise signal corrupting the desired signal but also reaching the secondary sensor delayed, making adaptive noise reduction the only feasible approach to reduce the noise from the corrupted signal.
 \begin{figure}[H]
     \centering
     \includegraphics[width=1.0\linewidth]{Bilder/fig_plot_3_wav_complex.png}
@@ -133,14 +133,14 @@ Therefore, the audio tracks from the previous example are now convolved with dif
     \caption{The raw noise signal recorded with two different sensors, showing the effect of different transfer functions on the signal}
     \label{fig:fig_plot_4_wav_complex.png}
 \end{figure}
-\noindent To evaluate the performance of the \ac{ANR} algorithm in this complex scenario, the corrupted signal is recorded with the primary sensor while the reference noise signal is recorded with secondary sensor. The filter output in Figure \ref{fig:fig_plot_1_wav_complex.png} indicates, that the \ac{ANR} algorithm is still capable of significantly reducing the noise from the corrupted signal, even with the reference noise signal being different from the corruption noise signal. 
+\noindent To evaluate the performance of the \ac{ANR} algorithm in this complex scenario, the corrupted signal is recorded with the primary sensor while the reference noise signal is recorded with secondary sensor. The filter output and \ac{SNR}-Ratio in Figure \ref{fig:fig_plot_1_wav_complex.png} display with 5.14 dB a significantly worse performance compared to the previous use case. This bevavior is perfectly explainable by the fact, that the introduced delay is taking the small 16 tap filter already to its limit to adapt effectively, as the noise signal is already changing significantly after 2 ms. A longer filter would be required to adapt effectively, especially if the noise signal would show a higher dynamics.
 \begin{figure}[H]
     \centering
     \includegraphics[width=1.0\linewidth]{Bilder/fig_plot_1_wav_complex.png}
     \caption{Desired signal, corrupted signal, reference noise signal and filter output of the complex \ac{ANR} use case}
     \label{fig:fig_plot_1_wav_complex.png}
 \end{figure}
-\noindent The error signal in Figure \ref{fig:fig_plot_2_wav_complex.png} shows, as expected, a slightly wore performance to the previous intermediate use case, indicating that the \ac{ANR} algorithm is confronted by a more challening task. The performance decrease can be explained by the fact, that the transfer functions applied to the signals have attenuated certain frequency components of the noise signal, making it harder for the \ac{ANR} algorithm to isolate and reduce the noise from the corrupted signal. Also, the corruption noise signal is reduced in amplitude, whereas the reference noise signal is amplified in certain frequency areas. Still, the \ac{SNR}-Gain of 6.15 dB still indicates a quite sucessful noise reduction, even in this more complex scenario.
+\noindent The error signal in Figure \ref{fig:fig_plot_2_wav_complex.png} shows, as expected, also a increased amplitude compared to the previous intermediate use case, indicating that the \ac{ANR} algorithm is confronted by a more challening task. Still, the \ac{SNR}-Gain of 5.14 dB still indicates a quite sucessful noise reduction, even with just 16 taps in this more complex scenario.
 \begin{figure}[H]
     \centering
     \includegraphics[width=1.0\linewidth]{Bilder/fig_plot_2_wav_complex.png}