5.3

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chapter_04.tex

@@ -253,8 +253,8 @@ C_{apply\_fir\_filter} = N + 12 \\
 C_{update\_output} = 1 \\
  \label{equation_c_4}
 C_{update\_filter\_coefficient} = \frac{1}{U}(6*N + 8)\\
-C_{write\_output} = 5 \\
  \label{equation_c_5}
+C_{write\_output} = 5 \\
 \end{gather}
 \noindent By inserting the sub-function costs into the total computing effort formula, Equation \ref{equation_computing} can now be expressed as:
 \begin{equation}
@@ -262,6 +262,11 @@ C_{write\_output} = 5 \\
  C_{total} = N + \frac{6*N+8}{U} + 34
 \end{equation}
 Equation \ref{equation_computing_final} now provides an estimation of the necessary computing effort for one output sample in relation to the filter length $N$ and the update rate of the filter coefficients $1/U$. This formula can now be used to estimate the needed computing power (and therefore the power consumption) of the \ac{DSP} core for different parameter settings, alowing to find an optimal parameter configuration in regard of the quality of the noise reduction and the power consumption of the system.
-
+\begin{figure}[H]
+    \centering
+    \includegraphics[width=1.0\linewidth]{Bilder/fig_c_total.png}
+    \caption{Dependence of the total computing effort on the filter length $N$ and update rate $1/U$.}
+    \label{fig:fig_c_total.png}
+\end{figure}
 
 

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chapter_05.tex

@@ -1,4 +1,5 @@
 \section{Performance evaluation of different implementation variants}
+\subsection{Verification of the \ac{DSP} implementation}
 To verify the general performance of the \ac{DSP}-implemented \ac{ANR} algorithm, the complex usecase of the high-level implemenation is utilized, which includes, again, a 16-tap \ac{FIR} filter and an update of the filter coefficients every cycle. In contary to the high-level implementation, the coeffcient convergence is now not included in the evaluation anymore, but the metric for the \ac{ANR} performance stays the same as the \ac{SNR} improvement.
 \begin{figure}[H]
     \centering
@@ -14,27 +15,51 @@ To verify the general performance of the \ac{DSP}-implemented \ac{ANR} algorithm
 \end{figure}  
 \noindent Figure \ref{fig:fig_plot_1_dsp_complex.png} and \ref{fig:fig_plot_2_dsp_complex.png} show the results of the complex \ac{ANR} use case, simulated on the \ac{DSP}. The \ac{SNR} improvement of 5.92 dB is similar to the one of the high-level implementation, which is 5.14 dB. The small difference can be explained by the fact that the \ac{DSP} implementation is based on fixed-point arithmetic, which leads to a slightly different convergence behavior. Nevertheless, the results show that the \ac{DSP} implementation of the \ac{ANR} algorithm is able to achieve a similar performance as the high-level implementation, again indicating the fact, that 16 filter coefficients are insufficent to filter out a complex, phase-shifted noise signal. The next step is of evaluate the performance of the \ac{DSP} implementation in terms of computational efficiency under different scenarios.
 \subsection{Computational efficiency evaluation}
-\noindent For the evaluation of the computational efficiency, different signal combinations, which are to be expected everyday situiations for a \ac{CI} patient, are considered. This approach rules out, that a certain combination of signals is not representative for the overall performance of the \ac{ANR} algorithm.
+\noindent The main focus for evaluating the computational efficiency is the determination of the optimal filter length. To achieve this goal, different signal combinations, which are to be expected everyday situiations for a \ac{CI} patient, are considered. This approach rules out, that a certain combination of signals is not representative for the overall performance of the \ac{ANR} algorithm.
 The desired signal of a male voice over speaker is now corrupted with 5 different noise signals:
 \begin{itemize}
-    \item Breathing noise: Already used in the high-level implementation, this noise signal is a typical noise source for \ac{CI} patients, especially in quiet environments. It consists out of slowly rising and falling peaks.
-    \item Coughing noise: This noise signal is generated by coughing and consists out few, but long lasting peaks.
-    \item Scratching noise: This noise signal is generated by scratching some material, like the hair or clothes. It consists out of a high number of sharp peaks.
-    \item Drinking Noise: This noise signal is generated by drinking and consists out of a low number of peaks, which are not as sharp as the ones of the scratching noise, but still more sharp than the ones of the breathing and coughing noise.
-    \item Chewing Noise: This noise signal is generated by chewing and consists out of a high number of peaks of different amplitude.
+    \item Breathing noise: Already used in the high-level implementation, this noise signal is a typical noise source for \ac{CI} patients, especially in quiet environments. It consists out of slowly rising and falling maxima.
+    \item Coughing noise: This noise signal is generated by coughing and consists out few, but long lasting maxima, showing similarities to a rectangular function.
+    \item Scratching noise: This noise signal is generated by scratching some material with finger nails, like the hair or clothes. It consists out of a high number of sharp peaks.
+    \item Drinking Noise: This noise signal is generated by swallowing a liquid and consists out of a low number of sharp peaks, featuring long pauses between them.
+    \item Chewing Noise: This noise signal is generated by consuming food and consists out of a high number of peaks of different amplitude.
 \end{itemize}
-The vizualization of the noise signals is shown in figure \ref{fig:fig_noise_signals.png}.
+The vizualization of the noise signals is shown in Figure \ref{fig:fig_noise_signals.png}.
 \begin{figure}[H]
     \centering
     \includegraphics[width=1.0\linewidth]{Bilder/fig_noise_signals.png}
     \caption{Noise signals used to corrupt the desired signal in the computational efficiency evaluation}
     \label{fig:fig_noise_signals.png}
 \end{figure}  
-The combination of stated sets delivers five different scenarious, everyone different in regard of it's challenges for the \ac{ANR} algorithm. For every scenario, the \ac{SNR}-Gain is calculated with an increasing set of filter coeffcients, ranging from 16 to 64.
+\noindent The combination of stated sets delivers five different scenarious, everyone different in regard of it's challenges for the \ac{ANR} algorithm. For every scenario, the \ac{SNR}-Gain is calculated with an increasing set of filter coeffcients, ranging from 16 to 64.
 \begin{figure}[H]
     \centering
     \includegraphics[width=1.0\linewidth]{Bilder/fig_snr_comparison.png}
-    \caption{Python simulation of the to be expected \ac{SNR}-Gain for different noise signals and filter lengths applied to the desired signal of a male speaker. The applied delay between the signals amounts 2ms. The graphes are smoothed by a third order savigol filter.}
+    \caption{Simulation of the to be expected \ac{SNR}-Gain for different noise signals and filter lengths applied to the desired signal of a male speaker. The applied delay between the signals amounts 2ms. The graphs are smoothed by a third order savigol filter.}
     \label{fig:fig_snr_comparison.png}
 \end{figure}  
-Figure \ref{fig:fig_snr_comparison.png} shows the expected \ac{SNR}-Gain for the different noise signals and filter lengths. The results shows, that a minimum filter length of about 32 taps is required, before (in any case) a rise in the \ac{SNR}-Gain can be observed. 
+\noindent Figure \ref{fig:fig_snr_comparison.png} shows the expected \ac{SNR}-Gain for the different noise signals and filter lengths. The results shows, that a minimum filter length of about 32 taps is required, before (in any case) a significant rise in the \ac{SNR}-Gain can be observed. This circustance can be explained by the fact, that the noise signals are phase-shifted, meaning, that the filter needs a certain length before it can react to the corruption noise signal. The results also show, that the \ac{SNR}-Gain is different for the different noise signals, which can be explained by the fact, that the noise signals have different characteristics, like the number of peaks, their frequency spectrum an their amplitude.\\ \\
+The mean \ac{SNR}-Gain of the different noise signals, also shown in Figure \ref{fig:fig_snr_comparison.png}, signals, that after reaching 95\% of the maximum \ac{SNR}-Gain, the \ac{SNR}-Gain increase is slowing down. This threshold is reached at a filter length of 45 taps. This indicates, that a filter length of 45 taps represents an optimal solution for a statisfying performance of the \ac{ANR} algorithm, while a further increase of the filter length does not lead to a significant increase of the \ac{SNR}-Gain. This is an important finding, as it allows to optimize the computational efficiency of the \ac{ANR} algorithm by choosing an appropriate filter length.
+\subsection{Evaluation of the computational load}
+\subsubsection{Full-Update implementation}
+\noindent Equation \ref{equation_computing_final} can now be utilized to calculate the needed cycles for the calculation of one sample of the filter output, using a filter length of 45 taps and an update of the filter coefficients every cycle. The needed cycles are calculated as follows:
+\begin{equation}
+\label{equation_computing_calculation}
+ C_{total} = 45 + \frac{6*45+8}{1} + 34 = 319 \text{ cycles}
+\end{equation}
+As already mentioned in the previous chapters, the sampling rate of the audio data provided to the \ac{PCM} interface amounts 20 kHz. The prefered clock frequency of the \ac{DSP} is set to 16 MHz, which means, that the \ac{DSP} core has cycle budget of
+\begin{equation}
+\label{equation_cycle_budget}
+    C_{budget} = \frac{16 MHz}{20 kHz} = 800 \text{ cycles}
+\end{equation}
+\noindent for one sample. With these two values, the load of the \ac{DSP} core can be calculated as follows:
+\begin{equation}
+\label{equation_load_calculation}
+    Load_{DSP} = \frac{C_{total}}{C_{budget}} = \frac{319 \text{ cycles}}{800 \text{ cycles}} = 39.88 \%
+\end{equation}
+\noindent The results, calculated in Equation \ref{equation_computing_calculation} to \ref{equation_load_calculation} can be summarized as follows:\\ \\ 
+With the optimal filter length of 45 taps and an update rate of the filter coefficients every cycle, the \ac{ANR} algorithm is able to achieve a \ac{SNR}-Gain of about 16,34 dB, averaged over different signal/noise combinatons. Under this circumstances, the computational load of the \ac{DSP} core amounts about 40\%, which means that 60\% of the time, which a new sample takes to arrive, it can be halted, and therefore, the overall power consumption can be reduced.\\ \\
+The initial signal/noise combination of a male speaker disturbed by a breathing noise, which is used for the verification of the \ac{DSP} implementation, delivers with 45 filter coefficients an \ac{SNR}-Gain of about 16,34 dB, which will be again used as an example for the next evaluation.
+\subsubsection{Reduced-update implementation}
+\subsubsection{Error-driven implementation}
+\subsection{Summary of the performance evaluation}

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chapter_06.tex

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+\section{Conclusion and outlook}

main.tex

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 \include{chapter_03}
 \include{chapter_04}
 \include{chapter_05}
+\include{chapter_06}
 \printbibliography
 \listoffigures