Bildbeschriftung und Bilder ausgebessert
This commit is contained in:
Patrick Hangl
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@@ -41,8 +41,8 @@ The flow diagram in Figure \ref{fig:fig_anr_logic} illustrates the logical flow
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return output, coefficient_matrix
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\end{lstlisting}
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\label{fig:fig_anr_code}
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\caption{High-level implementation of the \ac{ANR} algorithm in Python}
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\label{fig:fig_anr_code}
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\end{figure}
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\noindent The algorithm implementation shall now be put under test by different use cases to demonstrate the functionality and performance under different scenarios, varying from simple to complex ones. Every use case includes graphical representations of the desired signal, the corrupted signal, the reference noise signal, the filter output, the error signal and the evolution of selected filter coefficients over time. In contrary to a realistic setup, the desired signal is available, allowing to evaluate the performance of the algorithm in a clear way. The performance of the \ac{ANR} algorithm is evaluated based on the error between the desired signal and the filter output, complemented with the normalized integrated squared error.
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\subsection{Simple ANR use cases}
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@@ -150,8 +150,8 @@
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@@ -80,7 +80,7 @@ The memory initialization section starts with the definition of the interrupt re
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\label{fig:fig_dps_code_memory}
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\caption{Low-level implementation: Memory initialization and mapping}
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\end{figure}
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Figure \ref{fig:fig_compiler.jpg} shows an exemplary memory map of the input buffer array, taken from the compiler debugger. As the array is initialized as a 16 bit integer array, each element occupies 2 bytes of memory.
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\noindent Figure \ref{fig:fig_compiler.jpg} shows an exemplary memory map of the input buffer array, taken from the compiler debugger. As the array is initialized as a 16 bit integer array, each element occupies 2 bytes of memory.
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\begin{figure}[H]
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\centering
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\includegraphics[width=1.0\linewidth]{Bilder/fig_compiler.jpg}
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@@ -111,8 +111,8 @@ If the \ac{ARM} core requests a sample to be processed, it activates the \ac{DSP
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}
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}
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\end{lstlisting}
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\label{fig:fig_dps_code_mainloop}
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\caption{Low-level implementation: Main loop and interrupt handling}
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\label{fig:fig_dps_code_mainloop}
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\end{figure}
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\begin{figure}[H]
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\centering
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@@ -126,9 +126,22 @@ The calc()-function at the very end of the main process loop represents the hear
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\subsection{DSP-level implementation of the ANR algorithm}
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The ability to process audio samples in real-time on the \ac{DSP} core is strongly dependent on compiler-specific optimizations and hardware-specific implementation techniques, which allow a far more efficient execution of the algorithm compared to a native C implementation.
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\subsubsection{DSP-specific optimizations for real-time processing}
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Two important examples of optimization possibilities shall be outlined in the following, before the entire \ac{ANR} implementation on the \ac{DSP} is analyzed in regard of its performance.
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In the following, some examples of optimization possibilities shall be outlined , before the entire \ac{ANR} implementation on the \ac{DSP} is analyzed in regard of its performance.
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\paragraph{Logic operations}
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Logic operstions, such as finding the maximum or minimum of two values, are quite common in signal processing algorithms. However, their implementation in C usually involves conditional statements (if-else), which can be inefficient on certain architectures due to pipeline stalls.\\ \\
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The simple function shown in Figure \ref{fig:fig_dsp_code_find_max} returns the maximum of two given integer values. Processing this manual implementation on the \ac{DSP} takes 12 cycles to execute, while the intrinsic function of the \ac{DSP} compiler allows a 4-cycle execution.
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\begin{figure}[H]
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\centering
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\begin{lstlisting}[language=C]
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int find_max(int a, int b){
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return (a > b) ? a : b;
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}
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\end{lstlisting}
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\caption{Manual implementation of function, returning the maximum of two integer values, taking 12 cycles to execute. The intrinsic functions of the DSP compiler allows a 4-cycle implementation of such an operations.}
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\label{fig:fig_dsp_code_find_max}
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\end{figure}
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\paragraph{Cyclic array iteration}
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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.
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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.
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\begin{figure}[H]
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\centering
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\begin{lstlisting}[language=C]
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@@ -143,10 +156,15 @@ Basically every part of the \ac{ANR} algorithm relies on iterating through memor
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return new_pointer;
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}
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\end{lstlisting}
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\label{fig:fig_dps_code_cyclic_add}
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\caption{Manual implementation of a cyclic array iteration function in C.}
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\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.}
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\label{fig:fig_dsp_code_cyclic_add}
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\end{figure}
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\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.
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\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.
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\paragraph{Fractional fixed-point arithmetic}
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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.\\ \\
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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.\\ \\
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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.
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\subsubsection{Performance evaluation and quantization of the DSP implementation}
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@@ -1,4 +1,4 @@
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<mxfile host="app.diagrams.net" agent="Mozilla/5.0 (Windows NT 10.0; Win64; x64) AppleWebKit/537.36 (KHTML, like Gecko) Chrome/144.0.0.0 Safari/537.36" version="29.3.4">
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<mxCell id="ngw2JN3qWJ9t0b-mEEB_-5" parent="1" style="text;html=1;align=center;verticalAlign=middle;resizable=0;points=[];autosize=1;strokeColor=none;fillColor=none;" value="<span style="font-size: 20px;">y</span><span style="color: light-dark(rgb(0, 0, 0), rgb(255, 255, 255)); background-color: transparent; font-size: 20px;"><sub>[n]</sub></span><span style="font-size: 20px; background-color: transparent; color: light-dark(rgb(0, 0, 0), rgb(255, 255, 255));">&nbsp;=&nbsp;</span><span style="font-size: 20px;">w*x</span><span style="color: light-dark(rgb(0, 0, 0), rgb(255, 255, 255)); background-color: transparent; font-size: 20px;"><sub>[n]</sub></span>" vertex="1">
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1180
drawio/note_ANR.drawio
Normal file
1180
drawio/note_ANR.drawio
Normal file
File diff suppressed because it is too large
Load Diff
Reference in New Issue
Block a user