Überarbeitung, Check Prof
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Patrick Hangl
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@@ -91,9 +91,9 @@ The maximum offset bewteen the two graphs can be found at an updat rate of 0.39,
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\label{equation_load_calculation_reduced_update_1}
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\text{Load}_{\text{DSP}} = \frac{\text{C}_{\text{total}}}{\text{C}_{\text{budget}}} = \frac{188 \text{ cycles}}{800 \text{ cycles}} = 23.5 \%
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\end{equation}
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The interpretation of this results leads to the conclusion, that the most cost-effective way to reduce the load of the \ac{DSP} would be to reduce the update rate of the filter coefficients to 0.39. In the case of the benchmark signal/noise combination, this action nearly halfs the processor load from 44.6\% to 23.5\%, while only reducing the \ac{SNR}-Gain by rougly 31 \% from 9.47 dB to 6.40 dB. In the next step, the same analysis will be applied on all introduced noise signal, to get an idea of the general validity of the mad eobservation.
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The interpretation of this results leads to the conclusion, that the most cost-effective way to reduce the load of the \ac{DSP} would be to reduce the update rate of the filter coefficients to 0.39. In the case of the benchmark signal/noise combination, this action nearly halfs the processor load from 44.6\% to 23.5\%, while only reducing the \ac{SNR}-Gain by rougly 31 \% from 9.47 dB to 6.40 dB. In the next step, the same analysis will be applied on all introduced noise signal combinations, to get an idea of the general validity of the made observation.
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\subsubsection{Reduced-update implementation for multiple noise signals}
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Now the same evaluation as in the previous subchapter is conducted for the five introduced noise signals, with the difference, that now on the y-axis the performance gain (the distance between relative SNR-Gain and needed relative cycles/sample) instead of the \ac{SNR}-Gain is plotted.
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Now the same evaluation as in the previous subchapter is conducted for the five introduced noise signals in combination with the male speaker. The metric for the evaluation is now the performance gain (the distance between relative SNR-Gain and the needed relative cycles/sample) instead of the \ac{SNR}-Gain, as it allows a better picture of the cost-value ratio for the different update rates.
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\begin{figure}[H]
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\centering
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\includegraphics[width=1.0\linewidth]{Bilder/fig_gain_update_rate.png}
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@@ -116,7 +116,7 @@ Now the same evaluation as in the previous subchapter is conducted for the five
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\text{Load}_{\text{DSP}} = \frac{\text{C}_{\text{total}}}{\text{C}_{\text{budget}}} = \frac{168 \text{ cycles}}{800 \text{ cycles}} = 20.8 \%
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\end{equation}
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Equation \ref{equation_computing_calculation_reduced_update_2} and \ref{equation_load_calculation_reduced_update_2} confirm, that for an update rate of 0.32, a reduction of the \ac{DSP} load to 20.8\% can be achieved, correlating with a performance gain of 24.9\%. This means, that for all viewed scenarios, an update rate of 0.32 represents the best cost-value ratio, for reducing the load while geting the best possible noise reduction. The relative performance for all scenarios result in a mean \ac{SNR}-Gain reduction of 24.5\% from 11.54 dB to 8.72 dB, while the load of the \ac{DSP} core is reduced by about 53.4\% from 44.6\% to 20.8\%.
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\subsubsection{Computational load for reduced-update implementation}
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\subsubsection{Computational load of the reduced-update implementation}
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The most straight forward implmementation of a reduced update rate is through the use of a counter and a modulo operation, which checks, if for the current sample the filter coefficients has to be updated or not. The code must therefore be extended by two blocks which are responsible for additional computational load:
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\begin{gather}
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\label{equation_update_1}
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@@ -133,19 +133,18 @@ Incrementing the counter and checking if the counter has reached the update rate
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\label{equation_load_calculation_reduced_update_3}
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\text{Load}_{\text{DSP}} = \frac{\text{C}_{\text{total}}}{\text{C}_{\text{budget}}} = \frac{197 \text{ cycles}}{800 \text{ cycles}} = 24.6 \%
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\end{equation}
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The results from the updated equations show, that the computational load for an update rate of 0.32 increase substantially from 20.8\% to 24.6\% through the use of a counter and a modulo operation, as the latter is quite computational expensive. A better alternative would be the use of a bitwise check, but this would reduce the possible update rates to powers of 2.
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The results from the updated equations show, that the computational load for an update rate of 0.32 increase substantially from 20.8\% to 24.6\% through the use of a counter and a modulo operation, as the latter iscomputational quite expensive. A better alternative would be the use of a bitwise check, but this would reduce the possible update rates to powers of 2. In the case of the benchmark track, the load rises from 23.5\% to 27.1\%.
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\subsection{Evaluation of an error driven implementation}
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In contrary to the fixed update implementation of the previous chapter, the error-driven implementation is a more sophisticated approach, which focuses on an error metric, over which the decision for an coefficient update is made.
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The idea is, as the size update of the filter coefficients gets smaller, the benefit of updating them decreases. In practice, a closer look at the update of the filter coefficients is taken: As shown in Figure \ref{fig:fig_dsp_coefficient_cycle.jpg}, the size of the update of the filter coefficients is directly related to the error signal - if the error signal decreases, the update-size of the filter coefficients also decreases. \\ \\
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As the fixed update implementation is not able to detect such changes, the reduction in update frequency is applied in a static way, which means, that there are situations were it is beneficial and situations where it is not. The error-driven implementation, on the other hand, is able to detect such changing behaviorr and therefore can adapt the update frequency accordingly. Therefore, the error-driven implementation is expected to deliver a better cost-value ratio than the fixed update implementation.
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The idea is, as the update size of the filter coefficients gets smaller, the benefit of updating them decreases. In practice, a closer look at the update of the filter coefficients is taken: As shown in Figure \ref{fig:fig_dsp_coefficient_cycle.jpg}, the size of the update of the filter coefficients is directly related to the error signal - if the error signal decreases, the update-size of the filter coefficients also decreases. \\ \\
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As the fixed update implementation is not able to detect such changes, the reduction in update frequency is applied in a static way, which means, that there are situations were it is beneficial and situations where it is not. The error-driven implementation, on the other hand, is able to detect such changing behavior and therefore can adapt the update frequency accordingly. Therefore, the error-driven implementation is expected to deliver a better cost-value ratio than the fixed update implementation.
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\subsubsection{Error threshold implementation for the benchmark case}
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The chosen approach for this thessis the use a fixed error threshold. This means, that if the error signal remains below an, in advance set, certain threshold, the filter coefficients remain unchanged and are not updated. If the error signal exceeds the threshold, the filter coefficients are updated as in the full-update implementation. \\ \\ The crucial aspect of this approach, is the right choise of the error threshold, which is expected to be highly dependent on the acoustic situation. To get an idea of a beneficial error threshold, different values are initially evaluated for the already used benchmark case.\\ \\ The reduction in computational load must now be calculated for the whole audio track by the percentage of samples, where the error signal exceeds the threshold and therefore the coefficients are adapted. This means in detail, that if for a certain error threshold, 50000 of 200000 samples exceed said threshold, the filter coefficients are updated in 25\% of the samples - therefore the update rate of the filter coefficients amounts to 0.25. The result can therefore be expressed in the same way as for the fixed update implementation, where the update rate is directly calculated for one sample.
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The chosen approach for this thessis the use a fixed error threshold. This means, that if the error signal remains below an, in advance set, certain threshold, the filter coefficients remain unchanged and are not updated. If the error signal exceeds the threshold, the filter coefficients are updated as in the full-update implementation.\\ \\ The crucial aspect of this approach, is the right choise of the error threshold, which is expected to be highly dependent on the acoustic situation. To get an idea of a beneficial error threshold, different values are initially evaluated for the already used benchmark case.\\ \\ The reduction in computational load must now be calculated for the whole audio track by the percentage of samples, where the error signal exceeds the threshold and therefore the coefficients are adapted. This means in detail, that if for a certain error threshold, 50000 of 200000 samples exceed said threshold, the filter coefficients are updated in 25\% of the samples - therefore the update rate of the filter coefficients amounts to 0.25. The result can therefore be expressed in the same way as for the fixed update implementation, where the update rate is directly calculated for one sample.
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\begin{figure}[H]
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\centering
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\includegraphics[width=1.0\linewidth]{Bilder/fig_snr_error_threshold.png}
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\caption{Relative performance of the SNR-Gain, the cycles per samples and the DSP load in regard of the error threshold for the benchmark case. The baseline of 100\% is the full update implementation. The marked dots represent the results of the simulation for an explicit setup.}
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\caption{Relative performance of the SNR-Gain, the cycles per samples and the DSP load in regard of the error threshold for the benchmark case. The baseline of 100\% is the full update implementation. The marked dots represent the results of the simulation for an explicit setup.}
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\label{fig:fig_snr_error_threshold.png}
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\end{figure}
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\noindent Our benchmark track is evaluated for error tresholds ranging from 0 to 0.5. The results, represented in Figure \ref{fig:fig_snr_error_threshold.png}, show for small thresholds, especially smaller than 0.1, a highly beneficial behavior can be anticipated, where the \ac{SNR}-Gain is only slightly reduced, while the load of the \ac{DSP} core significantly drops. The maximum offset between the two graphs can be found at an error threshold of 0.02 - at this point, the coefficient adaption is only conducted in ~81400 of 200000 samples, which equivalents an update rate of about 41\%. Updating Equation \ref{equation_computing_calculation_full_update} and \ref{equation_load_calculation_full_update} therefore delivers:
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\begin{equation}
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@@ -156,9 +155,9 @@ The chosen approach for this thessis the use a fixed error threshold. This means
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\label{equation_load_calculation_error threshold_1}
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\text{Load}_{\text{DSP}} = \frac{\text{C}_{\text{total}}}{\text{C}_{\text{budget}}} = \frac{193 \text{ cycles}}{800 \text{ cycles}} = 24.1 \%
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\end{equation}
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The performance difference to reducing the update rate is already clearly for the benchmark case: With a similar \ac{DSP} load of 24.1\% (again, nearly half the load of the full update implementation), the \ac{SNR}-Gain is reduced by only 8.9\% from 9.47dB to 8.63 dB. The same analysis will be applied on all introduced noise signal, to get an idea of the general validity of the made observation.
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The performance difference to reducing the update rate is already clearly for the benchmark track: With a similar \ac{DSP} load of 24.1\% (again, nearly half the load of the full update implementation), the \ac{SNR}-Gain is reduced by only 8.9\% from 9.47dB to 8.63 dB. The same analysis will be applied on all introduced noise signal, to get an idea of the general validity of the made observation.
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\subsubsection{Error threshold implementaion for multiple noise signals}
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Again, the same evaluation as for the benchmark case is conducted for the five introduced noise signals, featuring the the performance gain instead of the \ac{SNR}-Gain as a performance metric.
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Again, the same evaluation as for the benchmark track is conducted for the five introduced noise signals, featuring the the performance gain instead of the \ac{SNR}-Gain as a evaluation metric.
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\begin{figure}[H]
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\centering
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\includegraphics[width=1.0\linewidth]{Bilder/fig_gain_error_threshold.png}
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@@ -171,7 +170,7 @@ Again, the same evaluation as for the benchmark case is conducted for the five i
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\caption{Absolute \ac{DSP} load in relation to the error threshold for different noise signals.}
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\label{fig:fig_load_error_threshold.png}
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\end{figure}
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\noindent Similar to the reduced update rate implementation, the obersvation made for every signal/noise combination is comparable to the benchmark case, but not the same. Figure \ref{fig:fig_gain_error_threshold.png} shows the performance gain for the five different scenarios. The most beneficial error threshold shifted noticeable to a value of 0.07. It´s interesting to notice, that the benchmark case seems to be a bit of an exception compared to the behavior of the other scenarios.\\ \\
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\noindent Similar to the reduced update rate implementation, the observation made for every signal/noise combination is comparable to the benchmark case, but not the same. Figure \ref{fig:fig_gain_error_threshold.png} shows the performance gain for the five different scenarios. The most beneficial error threshold shifted noticeable to a value of 0.07. It´s interesting to notice, that the benchmark case seems to be a bit of an exception compared to the behavior of the other scenarios.\\ \\
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A mean error threshold of 0.07 results in a mean update of 38244 out of 200000 samples, which equivalents an update rate of 19.1\%. The \ac{DSP} load for all scenarios is now not the same anymore, but still quite similar - Figure \ref{fig:fig_load_error_threshold.png} shows the absolute load of the \ac{DSP} core for an error threshold of 0.07 results in only 16.6\%.
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\begin{equation}
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\label{equation_computing_calculation_error_threshold_2}
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@@ -182,7 +181,7 @@ A mean error threshold of 0.07 results in a mean update of 38244 out of 200000 s
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\text{Load}_{\text{DSP}} = \frac{\text{C}_{\text{total}}}{\text{C}_{\text{budget}}} = \frac{132 \text{ cycles}}{800 \text{ cycles}} = 16.6 \%
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\end{equation}
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Equation \ref{equation_computing_calculation_error_threshold_2} and \ref{equation_load_calculation_error_threshold_2} confirm, that for an error threshold of 0.07, a reduction of the \ac{DSP} load to 16.6\% can be achieved, correlating with a performance gain of 48.4\%. This means, that for all viewed scenarios, an error threshold of 0.07 represents the best cost-value ratio, for reducing the load while geting the best possible noise reduction. The relative performance for all scenarios result in a mean \ac{SNR}-Gain reduction of 11.7\% from 11.54 dB to 10.19 dB, while the load of the \ac{DSP} core is reduced by about 62.8\% from 44.6\% to 16.6\%.
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\subsubsection{Computational load for error threshold implementation}
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\subsubsection{Computational load of the error threshold implementation}
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In contrary to the fixed update implementation, the error threshold implementation for a fixed error threshold does not require computational expensive operations: The threshold is implemented as a 32-bit integer which is simply checked for every sample by a single if-clause.
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\begin{gather}
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\label{equation_update_3}
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@@ -198,9 +197,35 @@ Equation \ref{equation_computing_calculation_error_threshold_3} and \ref{equatio
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\label{equation_load_calculation_error_threshold_3}
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\text{Load}_{\text{DSP}} = \frac{\text{C}_{\text{total}}}{\text{C}_{\text{budget}}} = \frac{142 \text{ cycles}}{800 \text{ cycles}} = 17.8 \%
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\end{equation}
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Contrary to the fixed update implementation, the computational load for an error threshold of 0.07 only shows only a minimal increase from 16.6\% to 17.8\% through the use of a computational cheap if-clause. This is a clear advantage compared to the fixed update implementation.
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Contrary to the fixed update implementation, the computational load for an error threshold of 0.07 only shows only a minimal increase from 16.6\% to 17.8\% through the use of a computational cheap if-clause. This is a clear advantage compared to the fixed update implementation. In the case of the benchmark track, the load rises from 24.1\% to 25.7\%.
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\subsection{Summary of the performance evaluation}
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The results of two analysis can be summarized as follows: \\ \\ With the optimal filter length of 45 taps and an update rate of the filter coefficients every cycle, the \ac{ANR} algorithm is able to achieve a \ac{SNR}-Gain of about 11.54 dB, averaged over all different signal/noise combinations. Under this circumstances, the computational load of the \ac{DSP} core amounts about 45\%, which means that 55\% of the time, which a new sample takes to arrive, it can be halted, and therefore, the overall power consumption can be reduced.\\ \\
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A simple method to further reduce the load of the \ac{DSP} core is to reduce the update frequency of the filter coeffcients. For the benchmark signal/noise combination, an update rate of 0.39 nearly halfs the processor load from 44.6\% to 23.5\%, while only reducing the \ac{SNR}-Gain by rougly 31 \% from 9.47 dB to 6.40 dB. For all viewed scenarios, an update rate of 0.32 represents the best cost-value ratio, for reducing the load while geting the best possible noise reduction - with a mean \ac{SNR}-Gain reduction of 24.5\% from 11.54 dB to 8.72 dB, while the load of the \ac{DSP} core is reduced by about 53.4\% from 44.6\% to 20.8\%. While the perfromance benefit of this approach is reasonable, the computanional effort of the implementation is significant - the 20.8\% total load rise to 24.6\%\\ \\
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A more sophisticated method to reduce the load of the \ac{DSP} core is to use an error-driven implementation, where the update of the filter coefficients is only conducted, if the error signal exceeds a certain threshold. For the benchmark case, with a similar \ac{DSP} load of 24.1\% the \ac{SNR}-Gain is reduced by only 8.9\% from 9.47dB to 8.63 dB. For all viewed scenarios, an error threshold of 0.07 represents the best cost-value ratio, for reducing the load while geting the best possible noise reduction - with a mean \ac{SNR}-Gain reduction of 11.7\% from 11.54 dB to 10.19 dB, while the load of the \ac{DSP} core is reduced by about 62.8\% from 44.6\% to 16.6\%. This substentional performance gain is bought by only a slight increase in computing effort - the 16.6\% total load rise only to 17.8\%\\ \\
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This result proofes, that an error-driven implementation of the \ac{ANR} algorithm is highly suitable to reduce the load needed for adaptive noise reduction in a \ac{CI} application, while still providing nearly 90\% of the maximum achievable performance under the viewed circumstances.
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A simple method to further reduce the load of the \ac{DSP} core is to reduce the update frequency of the filter coeffcients. For the benchmark signal/noise combination, an update rate of 0.39 nearly halfs the processor load from 44.6\% to 23.5\%, while only reducing the \ac{SNR}-Gain by rougly 31 \% from 9.47 dB to 6.40 dB. For all viewed scenarios, an update rate of 0.32 represents the best cost-value ratio, for reducing the load while geting the best possible noise reduction - with a mean \ac{SNR}-Gain reduction of 24.5\% from 11.54 dB to 8.72 dB, while the load of the \ac{DSP} core is reduced by about 53.4\% from 44.6\% to 20.8\%. While the perfromance benefit of this approach is reasonable, the computanional effort of the implementation is significant - the 20.8\% total load rise to 24.6\%. Figure \ref{fig:fig_snr_update_rate_new.png} shows the updated plot of the relative performance of the SNR-Gain, the cycles per samples and the DSP load in regard of the update rate for the benchmark case, where the higher load is indicated by the newly added continuous grahps. The initial graphs are still slightly visible allowing a better comparison of the two implementations.
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\begin{figure}[H]
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\centering
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\includegraphics[width=1.0\linewidth]{Bilder/fig_snr_update_rate_new.png}
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\caption{Updated plot of the relative performance of the SNR-Gain, the cycles per samples and the DSP load in regard of the update rate for the benchmark case. The higher load is indicated by the newly added continuous lines.}
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\label{fig:fig_snr_update_rate_new.png}
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\end{figure}
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\noindent A more sophisticated method to reduce the load of the \ac{DSP} core is to use an error-driven implementation, where the update of the filter coefficients is only conducted, if the error signal exceeds a certain threshold. For the benchmark case, with a similar \ac{DSP} load of 24.1\% (compared to the reduce update implementation), the \ac{SNR}-Gain is reduced by only 8.9\% from 9.47dB to 8.63 dB. For all viewed scenarios, an error threshold of 0.07 represents the best cost-value ratio - with a mean \ac{SNR}-Gain reduction of 11.7\% from 11.54 dB to 10.19 dB, while the load of the \ac{DSP} core is reduced by about 62.8\% from 44.6\% to 16.6\%. This substentional performance gain is bought by only a slight increase in computing effort - the 16.6\% total load rise only to 17.8\%\\ \\
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This result proofes, that an error-driven implementation of the \ac{ANR} algorithm is highly suitable to reduce the load needed for adaptive noise reduction in a \ac{CI} application, while still providing nearly 90\% of the maximum achievable performance under the viewed circumstances. Again, Figure \ref{fig:fig_snr_error_threshold_new.png} shows the updated plot of the relative performance of the SNR-Gain, the cycles per samples and the DSP load in regard of the error threshold for the benchmark case.
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\begin{figure}[H]
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\centering
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\includegraphics[width=1.0\linewidth]{Bilder/fig_snr_error_threshold_new.png}
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\caption{Updated plot of the relative performance of the SNR-Gain, the cycles per samples and the DSP load in regard of the error threshold for the benchmark case. The higher load is indicated by the newly added continuous lines.}
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\label{fig:fig_snr_error_threshold_new.png}
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\end{figure}
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\noindent The results of the performance evaluation for the different implementations of the \ac{ANR} algorithm are summarized in Table \ref{tab:summary_performance_evaluation}. The \ac{SNR} Gain is individually calculated for the most beneficial update rate or error threshold for the specific implementation, while the load of the \ac{DSP} core is calculated with the additional computational effort caused by the optimization.
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\begin{table}[h]
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\centering
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\begin{tabular}{|c|c|c|c|}
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\hline
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& \textbf{Full Update} & \textbf{Reduced Update} & \textbf{Error-Driven} \\ \hline
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\textbf{SNR-Gain Benchmark} &9.47 dB &6.40 dB &8.63 dB \\ \hline
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\textbf{DSP Load Benchmark} &44.6\% &27.1\% &25.7\% \\ \hline
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\textbf{SNR-Gain All Scenarios} &11.54 dB &8.72 dB &10.19 dB \\ \hline
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\textbf{DSP Load All Scenarios} &44.6\% &24.6\% &17.8\% \\ \hline
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\end{tabular}
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\caption{Summary of the performance evaluation for the different implementations of the ANR algorithm. The load of the DSP core is calculated with the additional computational effort of the optimization.}
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\label{tab:summary_performance_evaluation}
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\end{table}
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