端频率信号的离散频谱校正方法及应用基础研究

There exist mass of the following characteristic signals: the characteristic frequency of the signal are often located at the margin of spectrum, effective information is contained in the extremely low frequency components (frequencies below single DFT frequency resolution) or ultra high frequency components (frequency close to half the sampling frequency, that is, the Nyquist frequency).In addition, extremely low frequency components also include another case: when the signal duration is shorter, and the sampling frequency is larger, the signal characteristic frequency is relatively at the low-frequency position in the spectrum. Research shows that the impact of negative frequency on spectrum is generally not considered in existing discrete spectrum correction methods, which results in a bigger error, or even failure in the results of discrete spectrum correction. This program plans to put forward discrete spectrum correction methods for such margin signal, in order to give preciser spectrum parameters. Experiment based on Oil pump, Coriolis Mass Flow-meter and LFMCW radar system will be carried out to verify the proposed methods.

在状态监测与故障诊断、仪器仪表信号处理等领域，大量存在着以下一类信号：信号特征频率往往具有低于一个DFT频率分辨率（极端低频）、接近奈奎斯特频率（极端高频）等特点，其频率靠近分析频谱的两端，本项目称之为“端频率信号”。当采样频率相对信号频率较高、采样点数较少时，此类极短时信号也靠近频谱的极低频端。针对端频率信号，现有离散频谱校正方法效果很不理想，在精度、实时性等方面难以满足工程需要。本项目在分析端频率信号谱线干涉机理的基础上，提出计及负频率影响的极短时单频信号离散频谱融合校正方法、含单一频率分量和含密集频率分量的端频率信号离散频谱校正方法，并通过油料泵机组、科氏流量计和LFMCW雷达测距系统进行应用实验验证，着重解决端频率信号受负频率干涉严重、密集端频率信号频谱细化等关键问题，达到提高端频率信号离散频谱校正精度的目的，为状态监测与故障诊断、仪器仪表等工程应用提供相关信号处理理论和方法支撑。

本项目旨在提升位于频谱两端的端频率信号的离散频谱校正精度。在分析端频率信号谱线干涉机理的基础上，构建了计及负频率影响的极短时单频信号离散频谱融合模型；针对极低频信号，利用局部谱峰附近的三条谱线加Blackman窗，建立包含正负频率贡献的离散频谱校正模型，通过对模型的求解获得频率、幅值和相位校正公式。针对极高频信号，根据离散频谱的周期性，将极端高频信号表示为沿频率轴正反方向传播的波形叠加，建立包含正负频率贡献的离散频谱校正模型，依据窗函数性质对其变形，选择局部谱峰附近的三条谱线建立近似线性方程组，通过方程组的求解获得待测频率、幅值和相位校正公式。采用频段内扫描的方式对频谱校正公式进行了仿真验证，结果表明所提方法有效降低了负频率成分的干涉影响，对端频率信号的频率、幅值和相位校正有较高的精度。油料泵机组故障诊断和科氏流量计数字信号处理的应用验证，也显示了项目所提方法的有效性。项目资助发表论文2篇，待发表两篇（EI检索）。培养博士生1名，已经取得博士学位；培养硕士生3名，其中2名已经取得硕士学位。项目投入经费20万元，支出14.0590万元，各项支出基本与预算相符。剩余经费5.9410万元，剩余经费计划用于本项目研究后续支出。