5.2

chapter_03.tex

@@ -118,8 +118,9 @@ After the general functionality of the \ac{ANR} algorithm has been verified with
 \end{figure}
 \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 6.41 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 not only differs from the noise signal corrupting the desired signal, making adaptive noise reduction the only feasible approach to reduce the noise from the corrupted signal.
+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 utilized - but now they pass 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 corruption noise signal and the reference noise signal is introduced - this simulates the realsitic case, that the microphones are located on different locations, leading to a small delay due to traveling time of the signal. Now, an analytical solution is not possible anymore, as the signals are affected 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 on synchrone signals passing different singal paths.\\ \\
+Using  a sampling frequency of 20 kHz, a delay of 2 ms represents a shift of 40 samples. As the corrpution noise signal, which the alorithm tries to filter out of the corrupoted signal, is now delayed by these 40 samples, the filter needs more coefficients to aqquire a certain ''memory'' - this means, that the until now used 16 tap filter is not sufficient anymore. To prove the correct function of the \ac{ANR} algorithm, the filter length is adapted up to 55 taps. \\ \\
+The now introduced challenges ae 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 +134,14 @@ 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 and \ac{SNR}-Ratio in Figure \ref{fig:fig_plot_1_wav_complex.png} display with 6.98 dB a an even slightly better performance compared to the previous use case. This bevavior is explainable by the fact, that depending on the transfer functions of the sensors, for some signals the adaptation process might be more effective than for others.
+\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 10.26 dB an excellent performance. 
 \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, also a similar amplitude compared to the previous intermediate use case, indicating that the \ac{ANR} algorithm is still working fine. The \ac{SNR}-Gain of 6.98 dB indicates a quite sucessful noise reduction, even with just 16 taps in this more complex scenario.
+\noindent The error signal in Figure \ref{fig:fig_plot_2_wav_complex.png} shows, as expected, a small and further decreasing amplitude, indicating a nearly full removal of the corruption noise. 
 \begin{figure}[H]
     \centering
     \includegraphics[width=1.0\linewidth]{Bilder/fig_plot_2_wav_complex.png}