Korr 4

chapter_02.tex

@@ -2,12 +2,12 @@
 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.\\
-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.\\
+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} and its design- and 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.\\ \\
-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.\\ 
+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.\\ \\
-The term "signal interference" describes the overlapping of unwanted signals or noise with the desired signal, degrading the overall quality and intelligibility of the processed information. A simple example of signal interference is shown in Figure \ref{fig:fig_interference} - the noisy signal (top) consists out of several signals of different frequencies, representing both the desired signal and unwanted noise. The cleaned signal (bottom) shows the desired signal after unwanted frequencies has been cut off by a filter.\\ \\
+The term ``signal interference'' describes the overlapping of unwanted signals or noise with the desired signal, degrading the overall quality and intelligibility of the processed information. A simple example of signal interference is shown in Figure \ref{fig:fig_interference} - the noisy signal (top) consists out of several signals of different frequencies, representing both the desired signal and unwanted noise. The cleaned signal (bottom) shows the signal after unwanted frequencies has been cut off by a filter.\\ \\
 \begin{figure}[H]
     \centering
     \includegraphics[width=0.8\linewidth]{Bilder/fig_interference.jpg}
@@ -39,7 +39,7 @@ Before digital signal processing can be applied to an analog signal like human v
 \end{equation}
 where x[n] is the current sample and x[n-1] is the preceding sample. 
 \subsubsection{Time domain vs. frequency domain}
-A signal (either analog or digital) can be displayed and analyzed in two ways: the time domain and the frequency domain. The time domain shows the amplitude of the signal over time - like the sine waves from Figure \ref{fig:fig_interference}. If a Fast Fourier Transformation (FFT) is applied to the signal in the time spectrum, we receive the same signal in the frequency spectrum, now showing the spectral power present in the signal (refer to Figure \ref{fig:fig_fft}).\\ \\
+A signal (either analog or digital) can be displayed and analyzed in two ways: the time domain and the frequency domain. The time domain shows the amplitude of the signal over time - like the sine waves from Figure \ref{fig:fig_interference}. If a Fourier Transformation is applied to the signal in the time spectrum, we receive the same signal in the frequency spectrum, now showing the spectral power present in the signal (refer to Figure \ref{fig:fig_fft}).\\ \\
 \begin{figure}[H]
     \centering
     \includegraphics[width=0.8\linewidth]{Bilder/fig_fft.jpg}
@@ -63,7 +63,7 @@ During the description of transfer functions, the term ``filter'' was used but n
     \label{fig:fig_lowpass}
 \end{figure}
 \subsection{Filter designs}
-Before we continue with the introduction to the actual topic of this thesis, \ac{ANR}, two very essential filter designs need further explanation - the Finite Impulse Response- and Infinite Impulse Response filter. 
+Before we continue with the introduction of \ac{ANR}, two very essential filter designs need further explanation - the Finite Impulse Response- and Infinite Impulse Response filter. 
 \subsubsection{Finite Impulse Response filters}
 A \ac{FIR} filter, commonly referred to as a ``Feedforward Filter'' is defined through the property, that it uses only input values and not feedback from output samples to determine its filtering behavior - therefore, if the input signal is reduced to zero, the response of a \ac{FIR} filter reaches zero after a finite number of samples.\\ \\
 Equation \ref{equation_fir} specifies the input-output relationship of a \ac{FIR} filter - $x[n]$ is the input sample, $y[n]$ is output sample, and $b_0$ to $b_M$ the filter coefficients and M the length of the filter
@@ -112,7 +112,7 @@ In the 1930s, the first real concept of active noise cancellation was proposed b
 \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.\\ \\
+\ac{ANR} 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 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]
@@ -151,7 +151,7 @@ The goal of the adaptive filter is therefore to minimize this error signal over
 The minimization of the error signal $e[n]$ can be achieved by applying different error metrics and algorithms used to evaluate the performance of an adaptive filter, including:
 \begin{itemize}
 \item \ac{MSE}: This metric calculates the averaged square of the error between the expected value and the observed value over a predefined period. It is sensitive to large errors and is commonly used in adaptive filtering applications.
-\item \ac{LMS}: The \ac{LMS} is an algorithm, focused on minimizing the mean squared error by adjusting the filter coefficients iteratively based on the error signal by applying the gradient descent method. It is computationally efficient and widely used in real-time applications.
+\item \ac{LMS}: The \ac{LMS} is an algorithm, focused on minimizing the \ac{MSE} by adjusting the filter coefficients iteratively based on the error signal by applying the gradient descent method. It is computationally efficient and widely used in real-time applications.
 \item \ac{NLMS}: An extension of the \ac{LMS} algorithm that normalizes the step size based on the input signal, improving convergence speed.
 \item \ac{RLS}: This algorithm aims to minimize the weighted sum of squared errors, providing faster convergence than the \ac{LMS} algorithm but at the cost of higher computational effort.
 \end{itemize}
@@ -266,7 +266,7 @@ The \ac{LMS} algorithm therefore updates the filter coefficients $w[n]$ after ev
 \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. \\ \\
 The following definitions of the involved signals shall help to better understand the involved signals and their interactions:
 \begin{itemize}
-\item Desired signal: The wanted signal, like human voice, which shall be preserved.
+\item Desired signal: The wanted signal, like human voice, which shall be restored.
 \item Noise signal: The unwanted signal, like background noise, which shall be reduced.
 \item Recorded desired signal: The desired signal after passing the transfer function to the primary sensor.
 \item Corruption noise signal: The noise signal after passing the transfer function to the primary sensor.
@@ -288,7 +288,7 @@ x[n] = v[n] * (E_nB)
 \end{equation}
 where $v[n]$ is the noise signal at its source.\\ \\
 Another possible signal interaction could be the leakage of the desired signal into the secondary sensor, leading to the partial removal of the desired signal from the output signal. This case is not illustrated in Figure \ref{fig:fig_anr_implant} as it won't be further evaluated in this thesis, but shall be mentioned for the sake of completeness.\\ \\ 
-At this point, the theoretical background and the fundamentals of adaptive noise reduction have been adequately introduced and explained as necessary for the understanding of the following chapters of this thesis. The next chapter will now focus on practical high-level simulations of the \ac{ANR} algorithm under different circumstances to evaluate their performance in regard of noise reduction quality before the actual implementation on a low-power \ac{DSP} is conducted. 
+At this point, the theoretical background and the fundamentals of \ac{ANR} have been adequately introduced and explained as necessary for the understanding of the following chapters of this thesis. The next chapter will now focus on practical high-level simulations of the \ac{ANR} algorithm under different circumstances to evaluate their performance in regard of noise reduction quality before the actual implementation on a low-power \ac{DSP} is conducted.