MMS 3 Digital Signal Processor (DSP) Search Coil Magnetometer (SCM), Magnetic Field Power Spectral Density, Level 2 (L2), Slow Mode, 16 s Data

The MMS magnetic field power spectral density (BPSD) is computed onboard by the Digital Signal Processor (DSP). The fast Fourier transform (FFT) calculation is performed on a digitized version of analog signals from the Search Coil Magnetometer (SCM) in the SCM123 coordinate system (scm1 = - x sensor; scm2 = -z sensor; scm3 = -y sensor). This data product is computed in space from individual components that are not synchronized to the 1 second pulse. Therefore, the timing between channels can be inaccurate by a fraction of a second. The samples times are interval start times taken from the x component. The spectra are calculated via a 1024-point FFT algorithm on piecewise continuous sets of waveform data. Nine signals can be processed simultaneously. Six of the twelve DC-coupled E, DC-coupled V, or SCM signals (16384 samples/s) are selected for spectral processing at 100% duty cycle. In addition, the three AC-coupled signals (262,144 kS/s) each can be processed at 6.25% duty cycle. Each of the nine signals has 16, 1024-point FFT operations every second; the field-programmable gate array (FPGA) performs 144 FFTs per second. The FFT is performed by an arithmetic logic unit (ALU), which is controlled by a state machine. Both are hard-coded into the FPGA. The operation starts by applying a 1024-point Hanning window onto a waveform. Next, an FFT is implemented. The FFT is broken into a series of "butterfly" operations performed by the ALU. The result has real and imaginary data. Power spectra are calculated by taking the sum of squares of real and imaginary values (the ALU includes a multiplier), which produces a power spectrum with 512 frequency bins. The frequency bins are then combined to give pseudo-logarithmic frequency spacing (del f)/f. The spectra are reduced to 88 frequency bins with (del f)/f between 6% and 12% when possible. Narrow-band emissions can be fit to an accuracy of (del f)/f ~3%, allowing for an accurate determination of plasma density. The spectra can be averaged in time. The fastest reporting rate of any signal is 16 spectra per second. Reporting rates can be as slow a one spectra every 16 s (averaging 256 spectra). The averaging process has 48-bit accuracy to maximize the dynamic range. The amplitudes undergo a pseudo-logarithmic compression to an 8-bit number representing over 120 dB of dynamic range at ~5% precision.

MMS磁场功率谱密度（magnetic field power spectral density, BPSD）由星载数字信号处理器（Digital Signal Processor, DSP）完成计算。快速傅里叶变换（Fast Fourier Transform, FFT）的计算针对SCM123坐标系下搜索线圈磁强计（Search Coil Magnetometer, SCM）输出的模拟信号数字化版本执行，其中scm1 = -x传感器；scm2 = -z传感器；scm3 = -y传感器。该数据产品由未与1秒脉冲同步的单个分量在空间环境中计算得到，因此各通道间的时序误差可达几分之一秒量级。采样时刻取自x分量的区间起始时刻。频谱通过1024点FFT算法，对分段连续的波形数据集计算得到。系统可同时处理9路信号：12路直流耦合E、直流耦合V或SCM信号（采样率16384样本/秒）中可选取6路以100%占空比进行频谱处理；此外3路交流耦合信号（采样率262144千样本/秒）每路均可在6.25%占空比下完成处理。9路信号每秒各执行16次1024点FFT运算，而现场可编程门阵列（Field-Programmable Gate Array, FPGA）每秒可完成144次FFT运算。FFT运算由算术逻辑单元（Arithmetic Logic Unit, ALU）执行，该单元受状态机控制，二者均固化于FPGA内部。运算流程首先为波形施加1024点汉宁窗（Hanning window），随后执行FFT运算；整个FFT过程被分解为ALU执行的一系列蝶形运算，结果包含实部与虚部数据。功率谱通过对实部和虚部数值分别取平方后求和计算得到（ALU内置乘法器），由此生成包含512个频率通道的功率谱。随后对频率通道进行合并，以获得近似对数间隔的频率分布，其间隔满足(Δf)/f的形式。若条件允许，频谱会被压缩至88个频率通道，此时(Δf)/f的取值介于6%至12%之间。窄带辐射的拟合精度可达(Δf)/f≈3%，借此可精确推算等离子体密度。可对频谱进行时域平均处理：单路信号的最快上报速率为16次频谱/秒，最慢可低至每16秒输出1次频谱（即对256次频谱结果进行平均）。平均运算采用48位精度以最大化动态范围，幅值经过近似对数压缩后转换为8位数值，可在约5%的精度下覆盖超过120分贝的动态范围。