Multivariate Polynomial Minimization and Its Application in Signal Processing

We make a conjecture that the number of isolated local minimum points of a 2n-degree or (2n+1)-degree r-variable polynomial is not greater than n ^r when n 2. We show that this conjecture is the minimal estimate, and is true in several cases. In particular, we show that a cubic polynomial of r variables may have at most one local minimum point though it may have 2^r critical points. We then study the global minimization problem of an even-degree multivariate polynomial whose leading order coefficient tensor is positive definite. We call such a multivariate polynomial a normal multivariate polynomial. By giving a one-variable polynomial majored below a normal multivariate polynomial, we show the existence of a global minimum of a normal multivariate polynomial, and give an upper bound of the norm of the global minimum and a lower bound of the global minimization value. We show that the quartic multivariate polynomial arising from broad-band antenna array signal processing, is a normal polynomial, and give a computable upper bound of the norm of the global minimum and a computable lower bound of the global minimization value of this normal quartic multivariate polynomial. We give some sufficient and necessary conditions for an even order tensor to be positive definite. Several challenging questions remain open.     

Application of adaptive time-frequency decomposition in ultrasonic NDE of highly-scattering materials

In the paper, adaptive time-frequency decomposition by basis pursuit (BP) is utilized to improve ultrasonic flaw detection in highly-scattering materials as an alternative to the Wavelet Transform technique. The detection of ultrasonic pulses using the BP is described. Computer simulation was performed to verify the signal detection improvements for an ultrasonic wave embodied in white noise, and numerical results show good detection even for signal-noise ratio (SNR) of -18 dB. The improvement in detection is experimentally verified using cast steel samples with artificial flaws.     

Classification of Dansgaard–Oeschger climatic cycles by the application of similitude signal processing

In this work we have performed a detailed analysis, using signal processing tools, to study time series of data (temperature proxy) extracted from the GRIP ice-core records and we relate it with the evolution of atmospheric CO₂ within the last glacial period. Our method is based in considering the warm periods known as Dansgaard–Oeschger (D/O) events and posterior returns to the cold stage as a climatic cycle. After the warming phase, D/O events relax to the initial cold state in three different ways, what gives rise to three classes of cycles. Also, the Younger/Dryas–Bolling/Allerod (Y/D–B/A) cycle corresponds to one of the classes obtained. We have found that all cycles start with identical warming phases which seem completely unrelated to variations in CO₂ concentration. We discuss on the consequences for global climatology of such steady pattern of cycles.     

深水多波束测深系统脉冲压缩实时算法

线性调频信号是大时宽带宽积信号,通过脉冲压缩可提高探测距离和分辨率,已在深水多波束测深系统中得到广泛应用。针对深水多波束测深系统中脉冲压缩运算量大的问题,提出了一种基于分组的脉冲压缩实时算法。该算法对需要进行脉冲压缩的波束进行分组,每个节拍只计算一组波束,可大幅减少深水多波束测深系统脉冲压缩的运算时间,节省了处理器资源。该算法已成功应用于某深水多波束测深系统,经多次海试证明,工作稳定可靠。     

Graphene oxide-based biosensor for sensitive fluorescence detection of DNA based on exonuclease III-aided signal amplification

Based on the super fluorescence quenching efficiency of graphene oxide and exonuclease III aided signal amplification, we develop a facile, sensitive, rapid and cost-effective method for DNA detection. In the presence of target DNA, the target-probe hybridization forms a double-stranded structure and exonuclease III catalyzes the stepwise removal of mononucleotides from the blunt 3′ termini of probe, resulting in the recycling of the target DNA and signal amplification. Therefore, our proposed sensor exhibits a high sensitivity towards target DNA with a detection limit of 20 pM, which was even lower than previously reported GO-based DNA sensors without enzymatic amplification, and provides a universal sensing platform for sensitive detection of DNA.     

Comparison of the performance of three ion mobility spectrometers for measurement of biogenic amines

The performance of three different types of ion mobility spectrometer (IMS) devices: GDA2 with a radioactive ion source (Airsense, Germany), UV-IMS with a photo-ionization source (G.A.S. Germany) and VG-Test with a corona discharge source (3QBD, Israel) was studied. The gas-phase ion chemistry in the IMS devices affected the species formed and their measured reduced mobility values. The sensitivity and limit of detection for trimethylamine (TMA), putrescine and cadaverine were compared by continuous monitoring of a stream of air with a given concentration of the analyte and by measurement of headspace vapors of TMA in a sealed vial. Preprocessing of the mobility spectra and the effectiveness of multivariate curve resolution techniques (MCR-LASSO) improved the accuracy of the measurements by correcting baseline effects and adjusting for variations in drift time as well as enhancing the signal to noise ratio and deconvolution of the complex data matrix to their pure components. The limit of detection for measurement of the biogenic amines by the three IMS devices was between 0.1 and 1.2 ppm (for TMA with the VG-Test and GDA, respectively) and between 0.2 and 0.7 ppm for putrescine and cadaverine with all three devices. Considering the uncertainty in the LOD determination there is almost no statistically significant difference between the three devices although they differ in their operating temperature, ionization method, drift tube design and dopant chemistry. This finding may have general implications on the achievable performance of classic IMS devices.     

From a point-like to an arbitrarily shaped sample: A survey of equations for electron paramagnetic resonance signal intensity calculations

A set of original, analytical equations useful for theoretical calculation of the electron paramagnetic resonance (EPR) signal intensity are presented for the multitude of sample shapes, which range from point-like, line-like, planar, rectangular, cubical, circular, cylindrical, spherical to an irregularly shaped sample. The samples can be situated at any available position within the prescribed part of the microwave cavity (a central cylinder of diameter 11 mm and length 23.5 mm, in either a Bruker single TE₁₀₂ or double TE₁₀₄ rectangular cavity, with the modulation coils situated in the left and right side cavity walls, which is connected to a X-band, field-modulated CW Bruker EPR spectrometer). The theoretical computations of EPR signal intensity can be used in the computer simulations in which: (i) the EPR signal intensity profiles are constructed; (ii) the optimal sample positions in the cavity to give a maximum value of signal intensity are found; (iii) the errors associated with sample positioning within the cavity when compared to a second sample of a different size, shape or position are studied.     

一种在色噪声环境下的信号检测方法

为了抑制蛟龙号载人潜水器水声通信受母船色噪声干扰的影响,本文提出了一种统计匹配滤波器在色噪声环境下使用的新方法,它通过将接收信号映射到一个生成子空间中进行信号检测,可提高输出水声通信信号的信噪比。受客观条件限制,向阳红09船——蛟龙号载人潜水器的试验母船噪声环境比较恶劣,对水声通信产生了较强的干扰。如何在向阳红09船的这种强、色噪声环境下,提升水声同步信号的检测能力,对提高水声通信的可靠性是非常有帮助的。实际采集试验数据分析结果验证了该检测算法比传统匹配滤波器有更强的信号检测能力。     

基于Hilbert变换的水下多源声信号频率的相干探测

为实现水下中低频声信号的探测识别,通过研究水下多声源相干探测信号的特征,理论上给出了相干探测信号频谱混叠情况下的特征表达式,并提出了一种基于Hilbert变换的信号解调处理方法,实现了水下多声源相干探测信号频谱混叠情况下各声源发声频率的解调.该方法将探测信号经过滤波平滑处理之后进行Hilbert变换,得到信号的解析形式,然后对解析信号模值的平方进行二次滤波平滑等处理,分离混叠在一起的频带,将得到的信号进行频谱分析,根据频移值计算得到水下各个声源的发声频率.在光学暗室下搭建激光相干探测系统,对2~6kHz的水下声信号进行实验,实验结果表明,该方法可以有效分离探测信号中混叠在一起的信号频带,并准确提取各水下声信号的发声频率,频率提取重复性不大于2.5Hz.     

一种多功能信号源系统设计

针对单一信号源无法满足测试需求的现状,提出了一种新型多功能信号源系统设计方案;详细阐述了信号源系统的硬件及软件设计,方案基于标准化、高速、可靠性三方面的考虑,硬件环境基于Compact PCI工控计算机,设计了3U CPCI结构的信号源板卡,配套软件采取模块化设计;该方案可实现多类型、多通道的高精度、高可靠性信号的独立输出和同时输出;实验结果表明,该多功能信号源系统稳定性好、可靠性高、使用便捷,满足设计需求。