Korr 3

chapter_02.tex

@@ -3,8 +3,7 @@ The following subchapters shall supply the reader with the theoretical foundatio
 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.\\
 At this point an introduction into \ac{ANR} follows, including a short overview of the most important steps in history, the general concept of \ac{ANR}, its design possibilities and its optimization possibilities in regard of error calculation.\\
-With this knowledge covered, a realistic signal flow diagram of an implanted \ac{CI} system with corresponding transfer functions is designed, essential to implement \ac{ANR} on a low-power digital signal processor.\\
-At the end of chapter two, high-level Python simulations shall function as a feasibility demonstration of the recently presented theoretical background.\\ \\
+With this knowledge covered, a realistic signal flow diagram of an implanted \ac{CI} system with corresponding transfer functions is designed, essential to implement \ac{ANR} on a low-power digital signal processor.\\ \\
 Throughout this thesis, sampled signals are denoted in lowercase with square brackets (e.g. {x[n]}) to distinguish them from time-continuous signals (e.g. {x(t)}). Vectors are notated in lowercase bold font, whereas matrix are notated in uppercase bold font. Scalars are notated in normal lowercase font.\\ 
 \subsection{Signals and signal interference}
 A signal is a physical parameter (e.g. pressure, voltage) changing its value over time. Whereas in nature, a signal is always analog, meaning continuous in both time and amplitude, a digital signal is represented in a discrete form, being sampled at specific time intervals and quantized to finite amplitude levels.\\ \\
@@ -102,7 +101,7 @@ A higher number of needed coefficients implies, that the filter itself needs mor
 \subsection{Introduction to Adaptive Noise Reduction}
 \subsubsection{History}
 The necessity for the use of electric filters arose the first time in the beginnings of the 20th century with the development of the quite young fields of tele- and radio-communication. At his time, engineers used static filters, like low- or highpass filters, to improve transmission quality - this fundamental techniques allowed limiting the frequency spectrum, by cutting out certain frequencies like high-pitched noises or humming. From this time on, the development of new filter designs accelerated, for example with the soon-to-be developed LC-filter by Otto Zobel, an American scientist working at the telecommunication company AT\&T. Until then, the used filters were static, meaning they didn't change their behavior over time.\\ \\
-In the 1930s, the first real concept of \ac{ANC} was proposed by the German Physician Paul Lueg. Lueg patented the idea of two speakers emitting antiphase signals which cancel each other out. Though his patent was granted in 1936, back at the time, there was no technical possibility detect and process audio signals in a way, to make his noise cancellation actually work in a technical environment.\\ \\
+In the 1930s, the first real concept of active noise cancellation was proposed by the German Physician Paul Lueg. Lueg patented the idea of two speakers emitting antiphase signals which cancel each other out. Though his patent was granted in 1936, back at the time, there was no technical possibility detect and process audio signals in a way, to make his noise cancellation actually work in a technical environment.\\ \\
 20 years after Lueg's patent, Lawrence Fogel patented a practical concept of noise cancellation, intended for noise suppression in aviation - this time, the technical circumstances of the 1950s enabled the development of an aviation headset, lowering the overall noise experienced by pilots in the cockpit of a helicopter or an airplane by emitting a 180 degree phase shifted signal of the recorded background noise of the cockpit into the pilots' headset. (see Figure \ref{fig:fig_patent}).  
 \begin{figure}[H]
     \centering
@@ -110,11 +109,11 @@ In the 1930s, the first real concept of \ac{ANC} was proposed by the German Phys
     \caption{Reconstruction of Lawrence Fogel´s patent in 1960. \cite{source_patent}}
     \label{fig:fig_patent}
 \end{figure}
-\noindent In contrary to the static filters in the beginning of the century, the \ac{ANC} approach of Lueg and Widrow was far more advanced than just reducing a signal by a specific frequency portion like with the use of static filters, yet this technique still has their limitations as it is designed only to work within to a certain environment.\\ \\
+\noindent In contrary to the static filters in the beginning of the century, the active noise cancellation approach of Lueg and Widrow was far more advanced than just reducing a signal by a specific frequency portion like with the use of static filters, yet this technique still has their limitations as it is designed only to work within to a certain environment.\\ \\
 With the rapid advancement of digital signal processing technologies, noise cancellation techniques evolved from static, hardware-based filters and physical soundwave cancellation towards more sophisticated approaches. In the then 1970s, the concept of digital adaptive filtering arose, allowing digital filters to adjust their parameters in real-time based on the characteristics of the incoming signal and noise. This marked a significant leap forward, as it enabled systems to deal with dynamic and unpredictable noise environments - the concept of adaptive noise reduction was born.
 \subsubsection{The concept of adaptive filtering}
 Adaptive noise reduction describes an advanced filtering method based on an error-metric and represents a significant advancement over these earlier methods by allowing the filter parameters to continuously adapt to the changing acoustic environment in real-time. This adaptability makes \ac{ANR} particularly suitable for hearing devices, where environmental noise characteristics vary constantly.\\ \\
-Static filters, like low- and high-pass filters, as described in the previous subchapter, feature coefficients that remain constant over time. They are designed for known, predictable noise conditions (e.g., removing a steady 50 Hz hum). While these filters are efficient and easy to implement, they fail to function when noise characteristics change dynamically.\\ \\
+Static filters, like low- and high-pass filters, as described in the previous subchapter, feature coefficients that remain constant over time. They are designed for known, predictable noise conditions (e.g. removing a steady 50 Hz hum originating from a power supply). While these filters are efficient and easy to implement, they fail to function when noise characteristics change dynamically.\\ \\
 Although active noise cancellation and adaptive noise reduction share obvious similarities, they differ fundamentally in their application and signal structure. While active noise cancellation aims to physically cancel noise in the acoustic domain — typically before, or at the time, the signal reaches the ear — \ac{ANR} operates within the signal processing chain, attempting to extract the noisy component from the digital signal. In cochlear implant systems, the latter is more practical because the acoustic waveform is converted into electrical stimulation signals; thus, signal-domain filtering is the only feasible approach.
 \begin{figure}[H]
     \centering
@@ -261,7 +260,7 @@ The \ac{LMS} algorithm therefore updates the filter coefficients $w[n]$ after ev
  \begin{figure}[H]
     \centering
     \includegraphics[width=1.1\linewidth]{Bilder/fig_anr_implant.jpg}
-    \caption{Realistic implant design.}
+    \caption{Filter design for an implanted cochlear implant system with two signal sensors.}
     \label{fig:fig_anr_implant}
 \end{figure}
 \noindent Figure \ref{fig:fig_anr_hybrid} showed us the basic concept of an \ac{ANR} implementation, without a detailed description how the corrupted signal $d[n]$ and the reference noise signal $x[n]$ are formed. Figure \ref{fig:fig_anr_implant} now shows a more complete and realistic signal flow diagram of an implanted cochlear implant system, with two signal sensors and an adaptive noise reduction circuit afterwards. \\ \\