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The intrinsic functions of the DSP compiler allows a 4-cycle implementation of such an operations.} + \label{fig:fig_dsp_code_find_max} +\end{figure} \paragraph{Cyclic array iteration} -Basically every part of the \ac{ANR} algorithm relies on iterating through memory sections in a cyclic manner. In C, this is usually implemented by defining an array, containing the data, and a pointer, which is incremented after each access. When the pointer reaches the end of the array, it is reset to the beginning of the array again. This approach requires several different operations, such as pointer incrementation, if-clauses and for loops. +Basically every part of the \ac{ANR} algorithm relies on iterating through memory sections in a cyclic manner. In C, this is usually implemented by defining an array, containing the data, and a pointer, which is incremented after each access. When the pointer reaches the end of the array, it is reset to the beginning again. This approach requires several different operations, such as pointer incrementation, if-clauses and for-loops. \begin{figure}[H] \centering \begin{lstlisting}[language=C] @@ -143,10 +156,15 @@ Basically every part of the \ac{ANR} algorithm relies on iterating through memor return new_pointer; } \end{lstlisting} - \label{fig:fig_dps_code_cyclic_add} - \caption{Manual implementation of a cyclic array iteration function in C.} + \caption{Manual implementation of a cyclic array iteration function in C, taking the core 20 cycles to execute an pointer inremen of 1. The intrinsic functions of the DSP compiler allows a single-cycle implementation of such cyclic additions.} + \label{fig:fig_dsp_code_cyclic_add} \end{figure} -\noindent Figure \ref{fig:fig_dps_code_cyclic_add} shows a simple implementation of such a cyclic array iteration function in C, which updates the pointer to a new address. This implementation takes the \ac{DSP} 20 cycles to execute, while the already implemented compiler-optimized version only takes one cycle, making use of the specific architecture of the \ac{DSP} to perform the cyclic addition in a single operation. +\noindent Figure \ref{fig:fig_dsp_code_cyclic_add} shows a manual implementation of such a cyclic array iteration function in C, which updates the pointer to a new address. This implementation takes the \ac{DSP} 20 cycles to execute, while the already implemented compiler-optimized version only takes one cycle, making use of the specific architecture of the \ac{DSP} allowing such a single-cycle operation. +\paragraph{Fractional fixed-point arithmetic} +As already mentioned during the beginning of the current chapter, the used \ac{DSP} is a fixed point processor, meaning, that it does not support floating-point arithmetic natively. Instead, it relies on fixed-point arithmetic, which represents numbers as integers scaled by a fixed factor. This is a key requirement, as it allows the use of the implemented dual \ac{MAC} \ac{ALU}s. This approach is also faster and more energy efficient, and therefore more suitable for embedded systems. However, it also introduces challenges in terms of precision and range, which need to taken into account when conducting certain calculations.\\ \\ +To tackle this issues, the \ac{DSP} compiler provides intrinsic functions for fractional fixed-point arithmetic, such as a fractional multiplication function, which takes two 32-bit integers as input and return an already bit-shifted 64-bit output, representing the fractional multiplication result. This approach prevents the need for manual bit-shifting operations after each multiplication.\\ \\ +To support such operations, a 72-bit accumulator is provided, allowing to store intermediate 64-bit results of 32-bit multiplications without losing precision - the remaining 8 bit serve as an overflow space. If needed, a saturation function is also provided, to round the 64-bit result back to a 32-bit value. + \subsubsection{Performance evaluation and quantization of the DSP implementation} diff --git a/drawio/fig_anr.drawio b/drawio/fig_anr.drawio index d7f63da..aed0b8a 100644 --- a/drawio/fig_anr.drawio +++ b/drawio/fig_anr.drawio @@ -1,4 +1,4 @@ - + @@ -73,20 +73,20 @@ - + - - + + - - + + - - + + diff --git a/drawio/fig_anr_hybrid.drawio b/drawio/fig_anr_hybrid.drawio index 335474f..bf29614 100644 --- a/drawio/fig_anr_hybrid.drawio +++ b/drawio/fig_anr_hybrid.drawio @@ -1,4 +1,4 @@ - + @@ -80,20 +80,20 @@ - + - - + + - - + + - - + + diff --git a/drawio/fig_anr_implant.drawio b/drawio/fig_anr_implant.drawio index ca807fa..c3678fc 100644 --- a/drawio/fig_anr_implant.drawio +++ b/drawio/fig_anr_implant.drawio @@ -1,4 +1,4 @@ - + @@ -83,23 +83,23 @@ - + - + - + - - + + - - + + - - + + @@ -148,10 +148,10 @@ - + - + diff --git a/drawio/fig_fir.drawio b/drawio/fig_fir.drawio index 0edd067..8899c8d 100644 --- a/drawio/fig_fir.drawio +++ b/drawio/fig_fir.drawio @@ -1,140 +1,140 @@ - + - + - - + + - - + + - - + + - - + + - - - - + + - - - - - - - - - - - - - + + + + + + + + + + + + + + + - - + + - - + + - - + + - - + + - - + + - - + + - - + + - - + + - - + + - - + + - - + + - - - - + + + + - - + + - - - - + + + + - - + + - - + + - - + + - - + + - - + + - - + + - - + + diff --git a/drawio/fig_iir.drawio b/drawio/fig_iir.drawio index 65de116..89e60b7 100644 --- a/drawio/fig_iir.drawio +++ b/drawio/fig_iir.drawio @@ -1,173 +1,173 @@ - + - + - - + + - - + + - - + + - - + + - - + + - - + + - - + + - - - - + + + + - - - - + + + + - - + + - - + + - - + + - - + + - - + + - - + + - - + + - - + + - - + + - - + + - - + + - - + + - - + + - - - - + + + + - - - - + + + + - - + + - - + + - - + + - - + + - - + + - - + + - - + + - - - - + + + + - - + + - - + + - - + + - - + + - - + + - - + + diff --git a/drawio/fig_wien.drawio b/drawio/fig_wien.drawio index e8f7d63..9316511 100644 --- a/drawio/fig_wien.drawio +++ b/drawio/fig_wien.drawio @@ -1,4 +1,4 @@ - + @@ -43,19 +43,19 @@ - + - - + + - + - + diff --git a/drawio/note_ANR.drawio b/drawio/note_ANR.drawio new file mode 100644 index 0000000..72c1933 --- /dev/null +++ b/drawio/note_ANR.drawio @@ -0,0 +1,1180 @@ + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + +

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