Korr 5

chapter_01.tex

@@ -20,7 +20,7 @@ Usually, a \ac{CI} system consists out of an external processor with a microphon
     \label{fig:fig_electrode}
 \end{figure}
 \noindent As for any head worn hearing aid, the audio processor of a \ac{CI} system does not only pick up the desired ambient audio signal, but also any sort of interference noises from different sources. This circumstance leads to a decrease in the quality of the final audio signal for the user. Reducing this interference noise through adaptive noise reduction, implemented on a low-power digital signal processor, which can be powered within the electrical limitations of a CI system, is the topic of this master's thesis.
-\subsection{Implementation of Adaptive Noise Reduction in Cochlear Implant Systems}
+\subsection{Implementation of adaptive noise reduction in cochlear implant systems}
 The above problem description of noise interference shows the need of further improvement of \ac{CI} systems in this regard. For persons with a healthy hearing sense, the addition of noise to an observed signal may just mean a decrease in hearing comfort, whereas for aurally impaired people it can make the difference in the basic understanding of information. As everyday environments present fluctuating background noise - from static crowd chatter to sudden sounds of different characteristics — that can severely degrade speech perception, the ability to suppress noise is a crucial benefit for users of cochlear implant systems. \\ \\
 \ac{ANR} (also commonly referred as \ac{ANC}), is an advanced signal processing technique that adjusts the parameters of a digital filter to suppress unwanted noise from a signal while preserving the desired signal. In contrary to static filters (like a high- or low-pass filter), \ac{ANR} uses real-time feedback to adjust said digital filter to adapt to the current circumstances.\\ \\
 The challenge in the implementation of \ac{ANR} in \ac{CI} systems lies in the limited capacities. As the \ac{CI} system is powered by a small battery located in the audio processor, energy efficiency is crucial for a possible solution of the described problem of noise interference. Any approach to a reduction of interference noise must be highly optimized with regard to computing power and implemented on dedicated low-power hardware, being able to be powered within the limitations of a \ac{CI} system.\\ \\

chapter_02.tex

@@ -1,4 +1,4 @@
-\section{Theoretical Background}
+\section{Theoretical background}
 The following subchapters shall supply the reader with the theoretical foundation of digital signal processing to better understand the following implementation of \ac{ANR} on a low-power signal processor.\\ \\
 The chapter begins with the description of signals, the problem of them interfering and the basics of digital signal processing in general, covering fundamental topics like signal representation, transfer functions and filters.\\
 Filters are used in various functional designs, therefore a short explanation into the concepts of Finite Impulse Response- and Infinite Impulse Response filters is indispensable.\\
@@ -46,7 +46,7 @@ A signal (either analog or digital) can be displayed and analyzed in two ways: t
     \caption{Sampled digital signal in the time spectrum and in the frequency spectrum. \cite{source_dsp_ch1}}
     \label{fig:fig_fft}
 \end{figure}
-\subsubsection{Transfer Functions and filters}
+\subsubsection{Transfer functions and filters}
 When we discuss signals in a mathematical way, we need to explain the term ``transfer function''. A transfer function is a mathematical representation of an abstract system that describes how an input signal is transformed into an output signal. This could mean a simple amplification or a phase shift applied to an input signal.
 \begin{figure}[H]
     \centering

chapter_03.tex

@@ -1,7 +1,7 @@
 \section{High level simulations}
 The main purpose of the high-level simulations is to verify and demonstrate the theoretical approach of the previous chapters and to evaluate the performance of the proposed algorithms under various conditions.  The following simulations include different scenarios such as, different types of noise signals and different considerations of transfer functions. The goal is to verify different approaches before taking the step to the implementation of said algorithms on the low-power \ac{DSP}.\\ \\
 The implementation is conducted in Python, which provides a flexible environment for numerical computations and data visualization. The simulation is graphically represented using the Matplotlib-library. 
-\subsection{Adaptive Noise Reduction algorithm implementation}
+\subsection{Adaptive noise reduction algorithm implementation}
 The high-level implementation of the \ac{ANR} algorithm follows the theoretical framework outlined in Subchapter 2.5, specifically Equation \ref{equation_lms}. The algorithm is designed to adaptively filter out noise from a desired signal using a reference noise signal. The implementation of the \ac{ANR} function includes the following key steps:
 \begin{itemize}
     \item Initialization: Define arrays to store the reference noise samples (Sample Line), the filter coefficients (Filter Line), the processed output samples (output), and the updated filter coefficients (coefficient\_matrix) over time. Then a sequence of input samples is processed iteratively.

chapter_05.aux

@@ -21,7 +21,7 @@
 \acronymused{ANR}
 \acronymused{SNR}
 \acronymused{ANR}
-\@writefile{toc}{\contentsline {subsection}{\numberline {5.2}Evaluation of a Full-update implementation}{62}{}\protected@file@percent }
+\@writefile{toc}{\contentsline {subsection}{\numberline {5.2}Evaluation of a full-update implementation}{62}{}\protected@file@percent }
 \newlabel{equation_computing_calculation_full_update}{{32}{62}{}{equation.32}{}}
 \acronymused{PCM}
 \acronymused{DSP}
@@ -34,7 +34,7 @@
 \acronymused{DSP}
 \acronymused{DSP}
 \acronymused{SNR}
-\@writefile{toc}{\contentsline {subsection}{\numberline {5.3}Evaluation of a Reduced-update implementation}{63}{}\protected@file@percent }
+\@writefile{toc}{\contentsline {subsection}{\numberline {5.3}Evaluation of a reduced-update implementation}{63}{}\protected@file@percent }
 \@writefile{toc}{\contentsline {subsubsection}{\numberline {5.3.1}Reduced-update implementation for the benchmark case}{63}{}\protected@file@percent }
 \acronymused{DSP}
 \acronymused{SNR}

chapter_05.tex

@@ -24,7 +24,7 @@ The vizualization of the five described noise signals is shown in Figure \ref{fi
 \end{figure}  
 \noindent Figure \ref{fig:fig_snr_comparison.png} shows the expected \ac{SNR}-Gain for the different noise signals and filter lengths. The result confirms, 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 is highly contrary to the synchrone intermediate high level simulation, where a filter length of only 16 taps provided sufficient noise reduction. This circumstance can be explained by the fact, that the corruption noise signal is now delayed to the reference noise signal, meaning, that the filter needs a certain length before it can be sufficiently adapted. The results also show, that the \ac{SNR}-Gain is different for the different noise signals, indicating, that the noise signal´s different characteristics, like the number and duration of peaks, propose differing challenges for the \ac{ANR} algorithm.\\ \\
 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 - that threshold is reached at a filter length of 45 taps. This means, 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 in this setup. This is an important finding, as it allows optimizing the computational efficiency of the \ac{ANR} algorithm by choosing an appropriate filter length.
-\subsection{Evaluation of a Full-update implementation}
+\subsection{Evaluation of a 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_full_update}
@@ -43,7 +43,7 @@ As already mentioned in the previous chapters, the sampling rate of the audio da
 \noindent The results, calculated in Equation \ref{equation_computing_calculation_full_update} to \ref{equation_load_calculation_full_update} can also be recapped 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 11.54 dB, averaged over different signal/noise combinations. Under these circumstances, the computational load of the \ac{DSP} core amounts about 45\%, which means that 55\% 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, shall serve as a benchmark for the coming evaluations. With 45 filter coefficients it delivers a \ac{SNR}-Gain of about 9.47 dB.
-\subsection{Evaluation of a Reduced-update implementation}
+\subsection{Evaluation of a reduced-update implementation}
 \subsubsection{Reduced-update implementation for the benchmark case}
 The most straight-forward method to further reduce the computing effort for the \ac{DSP} core is to reduce the update frequency of the filter coeffcients. For every sample, the new filter coefficients are calculated, but not written to the into the Filter Line - this means, that the filter, calculated for the previous sample, is applied to the actual sample. Depending on the acoustic situation, the savings in computing power will most likely lead to a degredation of the noise reduction quality, depending on if the current situation is highly dynamic (and therefore would require a frequent update of the filter coefficients) or is rather static. Changing the update frequency, changes the denominator in Equation \ref{equation_c_5} and therefore in Equation \ref{equation_computing_final}.\\ \\
 As already mentioned, the reduction of the update rate is initially evaluated for the benchmark case (male speaker disturbed by a breathing noise) and then checked for general validity. Therefore, the \ac{SNR}-Gain of 9.47 dB with 45 filter coefficients represent 100\% achievable noise reduction with a maximum of 357 cycles (also 100\%) in the following figure.

main.tex

@@ -114,11 +114,11 @@ by \par
     \noindent The chosen method for noise reduction is the use of an adaptive filter combined with the Least Mean Square algorithm, which is a widely utilized method in this context. The evaluation of the performance is conducted via the Signal-Noise-Ratio (SNR)-Gain, which serves as a metric for the quality of the noise reduction. Several use cases (from simple to realistic) are analyzed to evaluate the output qualitiy under different conditions.\\ \\
     \noindent After confirming the general feasibility of the proposed method in a high-level Python implementation, the algorithm is implemented in C, using DSP compiler instrinsic functions to achieve real-time capability. The performance of the C implementation is then sucessfully compared to the initial high-level variant, showing only minor deviations.\\ \\
     \noindent With a working C implementation in place, a closer look on the achievable performance under full-update settings is taken, which serves as a benchmark-setting for the remaining thesis. The computational cost of the algorithm is evaluated in terms of the needed cycles to compute one audio sample, which can be expressed as a function of the filter length and the update rate.\\ \\
-    \noindent With a feasibile equation developed, several noise sources are put under test, to evaluatue the optimal filter length, which is a trade-off between the performance improvement and the computational cost. The ideal filter length is determined at 45 coeffcients, where about 95\% averaged \ac{SNR}-Gain can be achieved.\\ \\
+    \noindent With a feasible equation developed, several noise sources are put under test to evaluatue the optimal filter length, which is a trade-off between the performance improvement and the computational cost. The ideal filter length is determined at 45 coeffcients, where about 95\% averaged \ac{SNR}-Gain can be achieved.\\ \\
-    \noindent With the filter lenght set, the improvement of the algorithm is tackled, both for a benchmark track and different signal/noise scenarios.\\ \\
+    \noindent With the filter length set, the improvement of the algorithm is tackled, both for a benchmark track and different signal/noise scenarios.\\ \\
     \noindent The first approach is a reduction of the update rate. This strategy is able to significantly reduce the needed cycles, but with a simultanious considerable decrease in the SNR-Gain.\\ \\
-    \noindent The second approach is an error driven optimization, utilizing the idea of a fixed threshold for the error signal, over which the decision over an upgrade of the filter coefficients is made. This approach turns out to be a success, as it is able to achieve a significant reduction in the needed cycles, while only reducing the SNR-Gain by a small amount.\\ \\
+    \noindent The second approach is an error-driven optimization, utilizing the idea of a fixed threshold for the error signal, over which the decision over an upgrade of the filter coefficients is made. This approach turns out to be a success, as it is able to achieve a significant reduction in the needed cycles, while only reducing the SNR-Gain by a small amount.\\ \\
-    \noindent Therefore, the error driven optimization approach can be seen as the sucessful result of this thesis, as it is able to further improve an already real-time capable ANR algorithm by significantly reducing the computational load of the DSP core, while only slightly decreasing the performance improvement in terms of the SNR-Gain.\\ \\
+    \noindent Therefore, the error-driven optimization approach can be seen as the sucessful result of this thesis, as it is able to further improve an already real-time capable ANR algorithm by significantly reducing the computational load of the DSP core, while only slightly decreasing the performance improvement in terms of the SNR-Gain.\\ \\
 
 \end{abstract}
 \include{chapter_01}