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\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.\\
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\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