A common problem in many complex physical systems is the determination of pulsation modes from irregularly sampled time-series, and there is a wealth of signal processing techniques that are being applied to post-pulse and real-time data analysis in such complex systems. The aim of this report is studying the problem of detecting in real-time spatial periodicities in the spectrum of magnetic fluctuations in tokamaks, for which optimization of the algorithm run-time is essential. The main tool used hereafter will be the SparSpec algorithm, initially devised for astrophysical purposes and already applied to the analysis of magnetic fluctuation data in various tokamaks, both currently or previously operating (JET, TCV, Alcator C-mod) and under construction (ITER, DTT). For JET, the baseline version of the SparSpec algorithm, dubbed SS-H2, already regularly runs in real-time on a 1 ms clock for detecting Toroidal Alfvn Eigenmodes using synchronously-detected magnetic perturbation. It was noted that the solution is only slowly changing in time as the background plasma typically also slowly evolves. Therefore, as a specifically real-time acceleration tool, we will focus on the use of a memory with relaxation scheme, whereby solutions obtained at previous time points are used to provide weighted input constraints for the solution at the current time point. Use of the measurement uncertainties to weight the data, the spectral window and the ensuing penalization criterion (dubbed the SS-V5ν0 algorithm) is reported in a companion work. The behaviour of the SparSpec algorithm under a variety of simulated circumstances, and one actual test case from the JET tokamak, is analysed and appropriate conditions for the convergence of the memory-penalised solutions are derived. The tuning of the input parameters is discussed based on the results of our simulations. It is found that the implementation of SparSpec using such a memory with relaxation scheme is quite a complex procedure, and only when correctly optimized the results are superior, both in terms of the speed and the accuracy of the calculations, to those obtained with the SS-H2 and SS-V5ν0 versions of the SparSpec algorithm.

许多复杂物理系统中的一个常见问题是脉动模式的确定来自不规则采样的时间序列，并且有大量的信号处理技术被应用于这种复杂系统中的后脉冲和实时数据分析。本报告的目的是研究在托卡马克磁波动谱中实时检测空间周期性的问题，为此优化算法运行时间是必不可少的。此后使用的主要工具将是 SparSpec 算法，该算法最初是为天体物理目的而设计的，并且已经应用​​于分析各种托卡马克中的磁涨落数据，无论是当前还是以前运行（JET、TCV、Alcator C-mod）和在建（ITER） , DTT)。对于 JET，SparSpec 算法的基线版本，称为 SS-H2，已经定期在 1 ms 时钟上实时运行，以使用同步检测的磁扰来检测环形 Alfvn 本征模。注意到由于背景等离子体通常也缓慢演化，因此溶液仅随时间缓慢变化。因此，作为一个专门的实时加速工具，我们将重点介绍一个具有松弛方案的内存，其中在先前时间点获得的解决方案用于为当前时间点的解决方案提供加权输入约束。使用测量不确定度对数据、光谱窗口和随后的惩罚标准（称为 SS-V5 ν 0 算法）进行加权在一项配套工作中进行了报告。分析了 SparSpec 算法在各种模拟环境下的行为，以及来自 JET 托卡马克的一个实际测试案例，并推导出了内存惩罚解决方案收敛的适当条件。基于我们的模拟结果讨论了输入参数的调整。发现SparSpec的实现使用这样的带松弛的内存方案是一个相当复杂的过程，只有在正确优化时，结果在计算速度和精度方面都优于使用 SparSpec 算法的 SS-H2 和 SS-V5 ν 0 版本获得的结果。