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为了实现多光谱数据同步快速处理的功能,设计了利用FPGA完成同步控制,利用DSP完成NUFFT数据处理的FPGA+DSP混合架构,该架构的组成如图 2所示。
系统核心处理部分由FPGA+DSP组成,ADC采集得到的光谱数据通过FPGA的先入先出接口(first input first output,FIFO)采集进入同步动态随机存取内存(synchronous dynamic random-access memory, SDRAM)、双倍速率(double data rate, DDR)、闪存(flash memory, FLASH), 其中, WFIFO表示写入接口; RFIFO表示读出接口。再通过同步时钟的读FIFO进入DSP,由DSP完成光谱数据反演的数据处理。因为采集获得的光谱数据为浮点型数据,所以选用了TMS320C6748型DSP。该款DSP主频456MHz,是一款高性能浮点型信息处理器,包括8组32位并行处理单元,非常适合多光谱数据高速并行处理。其主控芯片采用哈佛结构,支持单周期多指令功能,并且其包括了丰富的外设,如外EMIF、通用型之输入输出(general-purpose input/output, GPIO)、通用定时器、主机并行接口(host port interface, HPI)等。
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由于多光谱数据中的中心波长位置及干涉条纹周期均不同,而经典FFT算法[19-20]只能对等间隔采样数据进行处理,所以采用NUFFT实现非均匀采样, 可减小由于输入数据插值造成的误差,并且可大幅缩短系统运算时间。非均匀干涉数据反演也可以理解成采用一组均匀傅里叶变换系数组合做近似的方式实现。寻求xk-q/2(k=0, …, q)满足:
$ {S_j}{\omega ^{jmc}} = \sum\limits_{[mc] - q/2}^{[mc] + q/2} {{x_{k - [mc]}}} (c){\omega ^{jk}} $
(1) 式中,m≥2,ω=exp[-i2π/(mN)],[mc]为与mc最接近的整数,c为采样点采集得到的数值,q为正偶数,v为非均匀采样点,Sj(j=-N/2, -N/2+1, …, N/2-1)为窗函数。在本系统中,针对多光谱数据进行采集与分析,数据在频域中表现为具有紧支撑性。故采用高斯窗函数,有:
$ \begin{array}{l} {S_j} = \exp \left[ { - b{{\left( {\frac{{2{\rm{ \mathit{ π} }}j}}{{\mu N}}} \right)}^2}} \right]j, \\ (j = - N/2, \cdots N/2 - 1) \end{array} $
(2) 式中,b为常数参量,μ为窗函数调节参量,μ∈(0, 1),将(1)式以矩阵形式表达:
$ \mathit{\pmb{A}}x(c)=\mathit{\pmb{v}}(c) $
(3) 式中,A为等效(1)式的相应矩阵,x(c)为干涉信号数据,ν(c)为干涉条纹数据矩阵。由于(1)式是超定方程组,不存在精确解,所以采用最小二乘法计算,获得x(c)的最小二乘解有:
$ x(c)={{\mathit{\pmb{F}}}^{-1}}\mathit{\pmb{a}}(c) $
(4) 式中,a(c)=AHν(c),F(m, N, q)=AHA(H代表共轭转置)。由上式推导可知,NUFFT的步骤为:(1)利用(3)式计算每个ωk(第k个ω,与(1)式中ω为同一变量)的展开系数xj(ωk); (2)计算傅里叶系数$ {\tau _l} = \sum\limits_{j, k, [{m_{\omega k}}] + j = l} {{\alpha _k} \times } \;{x_j}({\omega _k})$; (3)通过FFT计算:$ {T_j} = \sum\limits_{l = - mN/2}^{mN/2 - 1} {{\tau _l}} \exp \left( {\frac{{2{\rm{i \mathit{ π} }}jl}}{{mN}}} \right)$(4)将以上两步的值乘以比例系数,从而近似的非均匀FFT有:$ {{\tilde f}_j} = {T_j}S_j^{ - 1}$。
根据NUFFT的实现步骤,再结合FPGA控制获取的光谱数据,FPGA通过产生同步驱动时钟对多光谱数据进行同步采集。在模块中设计了只读存储器(read-only memory, ROM)与计数器,ROM用于保存时钟管理芯片对应额匹配码,在上电复位后由计数器完成对时间段的读取,数据处理采用NUFFT算法实现。若CCD获取的N点干涉信号是x(t),x′(t)是x(t)被插值以后的新数据组,f(c)是核函数, t表示时间,则对光谱反演的算法流程如图 3所示。
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实验装置由含多特征光谱的宽带光源、干涉模块、TVD3724型CCD、高速ADC采集模块、FPGA+DSP处理模块组成(Virtex-2型FPGA与TMS320C6748型DSP配合)。多特征激光器波长分别为632nm, 880nm和980nm,整体实物如图 7所示。
为了实现多光谱数据同步采集与处理的要求,实验中针对3个激光同时入射形成的混合干涉条纹进行解析处理。基于DSP的光谱处理结果如图 8a所示,针对同一混合光源采集得到的光谱数据采用Advantest公司的Q8344A型光谱仪进行对比,结果如图 8b所示。
本系统与光谱仪复现结果对比可知,本系统中由于采用了NUFFT算法,对于不同特征光谱的干涉条纹实施了分区采样与插值,所以复现后的特征光谱分布更清晰,旁瓣抑制效果十分明显,并且中心波长位置处信噪比更大。复现光谱的主要参量对比见表 1。
Table 1. Comparison of main parameters
No. the system spectrometer center
wavelength/nmsignal-to-
noise ratio/dBmcenter
wavelength/nmsignal-to-
noise ratio/dBm1 632.3 31.6 632.1 20.1 2 879.6 36.3 879.9 25.4 3 980.3 32.5 980.1 23.7 通过表 1中光谱复现主要参量可知,两种方式的中心波长准确度相近,光谱仪略优于本系统。而对于信噪比而言,本系统在3个特征波长位置上均明显优于对比用的光谱仪。由此可见,针对多光谱数据进行分段插值,再进行NUFFT处理,可以有效地提高光谱复现的精度。
基于NUFFT的多光谱数据同步采集与处理系统设计
Design of multi-spectral data synchronous acquisition and processing system based on NUFFT
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摘要: 为了可以同时获取多谱段光谱信息,并且多测试数据同步处理,设计了一种基于现场可编程门阵列+数据信号处理器的同步采集与处理系统。采用非均匀快速傅里叶变换(NUFFT)算法对包含目标信息的谱段采样进行了针对多谱段数据非均匀采样的理论分析和实验验证。针对632nm,880nm和980nm 3种不同激光波长同时实验测试,分别采用本系统与传统光谱分析算法进行了对比。结果表明,本系统在3个波长峰值位置上的信噪比分别是31.6dBm, 36.3dBm和32.5dBm,而传统光谱仪的信噪比仅为20.1dBm, 25.4dBm和23.7dBm,采用本系统硬件设计配合NUFFT算法可以有效增强多谱段光谱信息获取过程中的信噪比。本系统的处理速度更快,在多光谱快速处理方面具有一定的应用价值。
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关键词:
- 测量与计量 /
- 非均匀快速傅里叶变换 /
- 多光谱数据处理 /
- 现场可编辑程门阵列+数据信号处理器
Abstract: In order to simultaneously acquire multi-spectral spectral information and multi-test data synchronization processing, a synchronous acquisition and processing system based on field-programmable gate array(FPGA)+digital signal processor(DSP) was designed. The non-uniform fast Fourier transform (NUFFT) algorithm was used to sample the spectral segments containing the target information, and the theoretical analysis and experimental verification for the non-uniform sampling of multi-spectral data were carried out. The experiments were respectively carried out simultaneously for three different laser wavelengths of 632nm, 880nm, and 980nm. The system was compared with the traditional spectral analysis algorithm. The test results show that the signal-to-noise ratio of the system at the peak position of three wavelengths is 31.6dBm, 36.3dBm, and 32.5dBm, respectively, while the signal-to-noise ratio of the traditional spectrometer is only 20.1dBm, 25.4dBm, and 23.7dBm. It can be seen that the hardware design of the system and the NUFFT algorithm can effectively enhance the signal-to-noise ratio in the process of acquiring multi-spectral spectral information. At the same time, the processing speed of the system is also faster, and it has certain application value in multi-spectral fast processing. -
Table 1. Comparison of main parameters
No. the system spectrometer center
wavelength/nmsignal-to-
noise ratio/dBmcenter
wavelength/nmsignal-to-
noise ratio/dBm1 632.3 31.6 632.1 20.1 2 879.6 36.3 879.9 25.4 3 980.3 32.5 980.1 23.7 -
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