Solder joint defects classification using the Log-Gabor Filter, the Discrete Wavelet Transform and the Discrete Cosine Transform

Inspection of solder joints has been a critical process in the electronic manufacturing industry to reduce manufacturing cost, improve yield, and ensure project quality and reliability. This paper proposes the use of the Log-Gabor filter bank, Discrete Wavelet Transform and Discrete Cosine Transform for feature extraction of solder joint images on Printed Circuit Boards (PCBs). A distance based on the Mahalanobis Cosine metric is also presented for classification of five different types of solder joints. From the experimental results, this methodology achieved high accuracy and a well generalised performance. This can be an effective method to reduce cost and improve quality in the production of PCBs in the manufacturing industry.

Voice source characterization using pitch synchronous discrete cosine transform for speaker identification

A characterization of the voice source (VS) signal by the pitch synchronous (PS) discrete cosine transform (DCT) is proposed. With the integrated linear prediction residual (ILPR) as the VS estimate, the PS DCT of the ILPR is evaluated as a feature vector for speaker identification (SID). On TIMIT and YOHO databases, using a Gaussian mixture model (GMM)-based classifier, it performs on par with existing VS-based features. On the NIST 2003 database, fusion with a GMM-based classifier using MFCC features improves the identification accuracy by 12% in absolute terms, proving that the proposed characterization has good promise as a feature for SID studies. (C) 2015 Acoustical Society of America

Phase unwrapping algorithms, respectively, based on path-following and discrete cosine transform

This paper describes a path-following phase unwrapping algorithm and a phase unwrapping algorithm based on discrete cosine transform (DCT) which accelerates the Computation and suppresses the propagation of noise. Through analysis of fringe pattern with serious noises simulated in mathematic model, we make a contrast between path-following algorithm and DCT algorithm. The advantages and disadvantages or analytical fringe pattern are also given through comparison of two algorithms. Three-dimensional experimental results have been given to prove the validity of these algorithms. Despite DCT phase unwrapping technique robustness and speed in some cases, it cannot be unwrapping inconsistencies phase. The path-following algorithm can be used in automation analysis of fringe patterns with little influence of noise. (c) 2007 Elsevier GmbH. All rights reserved.

Discrete cosine transform generator for VLSI synthesis

A generator for the automated design of Discrete Cosine Transform (DCT) cores is presented. This can be used to rapidly create silicon circuits from a high level specification. These compare very favourably with existing designs. The DCT cores produced are scaleable in terms of point size as well as input/output and coefficient wordlengths. This provides a high degree of flexibility. An example, 8-point 1D DCT design, produced occupies less than 0.92 mm when implemented in a 0.35µ double level metal CMOS technology. This can be clocked at a rate of 100MHz.

Computation of discrete cosine transform using Clenshaw's recurence formula

Clenshaw’s recurrenee formula is used to derive recursive algorithms for the discrete cosine transform @CT) and the inverse discrete cosine transform (IDCT). The recursive DCT algorithm presented here requires one fewer delay element per coefficient and one fewer multiply operation per coeflident compared with two recently proposed methods. Clenshaw’s recurrence formula provides a unified development for the recursive DCT and IDCT algorithms. The M v e al gorithms apply to arbitrary lengtb algorithms and are appropriate for VLSI implementation.

Digital signal processing and digital system design using discrete cosine transform [student course]

The discrete cosine transform (DCT) is an important functional block for image processing applications. The implementation of a DCT has been viewed as a specialized research task. We apply a micro-architecture based methodology to the hardware implementation of an efficient DCT algorithm in a digital design course. Several circuit optimization and design space exploration techniques at the register-transfer and logic levels are introduced in class for generating the final design. The students not only learn how the algorithm can be implemented, but also receive insights about how other signal processing algorithms can be translated into a hardware implementation. Since signal processing has very broad applications, the study and implementation of an extensively used signal processing algorithm in a digital design course significantly enhances the learning experience in both digital signal processing and digital design areas for the students.

On the use of discrete cosine transforms for multicarrier communications

In this correspondence, the conditions to use any kind of discrete cosine transform (DCT) for multicarrier data transmission are derived. The symmetric convolution-multiplication property of each DCT implies that when symmetric convolution is performed in the time domain, an element-by-element multiplication is performed in the corresponding discrete trigonometric domain. Therefore, appending symmetric redun-dancy (as prefix and suffix) into each data symbol to be transmitted, and also enforcing symmetry for the equivalent channel impulse response, the linear convolution performed in the transmission channel becomes a symmetric convolution in those samples of interest. Furthermore, the channel equalization can be carried out by means of a bank of scalars in the corresponding discrete cosine transform domain. The expressions for obtaining the value of each scalar corresponding to these one-tap per subcarrier equalizers are presented. This study is completed with several computer simulations in mobile broadband wireless communication scenarios, considering the presence of carrier frequency offset (CFO). The obtained results indicate that the proposed systems outperform the standardized ones based on the DFT.

Gear dynamics monitoring using discrete wavelet transformation and multi-layer perceptron neural networks

This paper presents a multi-stage algorithm for the dynamic condition monitoring of a gear. The algorithm provides information referred to the gear status (fault or normal condition) and estimates the mesh stiffness per shaft revolution in case that any abnormality is detected. In the first stage, the analysis of coefficients generated through discrete wavelet transformation (DWT) is proposed as a fault detection and localization tool. The second stage consists in establishing the mesh stiffness reduction associated with local failures by applying a supervised learning mode and coupled with analytical models. To do this, a multi-layer perceptron neural network has been configured using as input features statistical parameters sensitive to torsional stiffness decrease and derived from wavelet transforms of the response signal. The proposed method is applied to the gear condition monitoring and results show that it can update the mesh dynamic properties of the gear on line.

Estimation of Symmetric Channels for Discrete Cosine Transform Type-I Multicarrier Systems: A Compressed Sensing Approach

The problem of channel estimation for multicarrier communications is addressed. We focus on systems employing the Discrete Cosine Transform Type-I (DCT1) even at both the transmitter and the receiver, presenting an algorithm which achieves an accurate estimation of symmetric channel filters using only a small number of training symbols. The solution is obtained by using either matrix inversion or compressed sensing algorithms. We provide the theoretical results which guarantee the validity of the proposed technique for the DCT1. Numerical simulations illustrate the good behaviour of the proposed algorithm.

The relationship between the auditory brain-stem response and its reconstructed waveforms following discrete wavelet transformation

Objective: To examine the relationship between the auditory brain-stem response (ABR) and its reconstructed waveforms following discrete wavelet transformation (DWT), and to comment on the resulting implications for ABR DWT time-frequency analysis. Methods: ABR waveforms were recorded from 120 normal hearing subjects at 90, 70, 50, 30, 10 and 0 dBnHL, decomposed using a 6 level discrete wavelet transformation (DWT), and reconstructed at individual wavelet scales (frequency ranges) A6, D6, D5 and D4. These waveforms were then compared for general correlations, and for patterns of change due to stimulus level, and subject age, gender and test ear. Results: The reconstructed ABR DWT waveforms showed 3 primary components: a large-amplitude waveform in the low-frequency A6 scale (0-266.6 Hz) with its single peak corresponding in latency with ABR waves III and V; a mid-amplitude waveform in the mid-frequency D6 scale (266.6-533.3 Hz) with its first 5 waves corresponding in latency to ABR waves 1, 111, V, VI and VII; and a small-amplitude, multiple-peaked waveform in the high-frequency D5 scale (533.3-1066.6 Hz) with its first 7 waves corresponding in latency to ABR waves 1, 11, 111, IV, V, VI and VII. Comparisons between ABR waves 1, 111 and V and their corresponding reconstructed ABR DWT waves showed strong correlations and similar, reliable, and statistically robust changes due to stimulus level and subject age, gender and test ear groupings. Limiting these findings, however, was the unexplained absence of a small number (2%, or 117/6720) of reconstructed ABR DWT waves, despite their corresponding ABR waves being present. Conclusions: Reconstructed ABR DWT waveforms can be used as valid time-frequency representations of the normal ABR, but with some limitations. In particular, the unexplained absence of a small number of reconstructed ABR DWT waves in some subjects, probably resulting from 'shift invariance' inherent to the DWT process, needs to be addressed. Significance: This is the first report of the relationship between the ABR and its reconstructed ABR DWT waveforms in a large normative sample. (C) 2004 International Federation of Clinical Neurophysiology. Published by Elsevier Ireland Ltd. All rights reserved.

Shift, scaling and derivative properties for the discrete cosine transform

A set of DCT domain properties for shifting and scaling by real amounts, and taking linear operations such as differentiation is described. The DCT coefficients of a sampled signal are subjected to a linear transform, which returns the DCT coefficients of the shifted, scaled and/or differentiated signal. The properties are derived by considering the inverse discrete transform as a cosine series expansion of the original continuous signal, assuming sampling in accordance with the Nyquist criterion. This approach can be applied in the signal domain, to give, for example, DCT based interpolation or derivatives. The same approach can be taken in decoding from the DCT to give, for example, derivatives in the signal domain. The techniques may prove useful in compressed domain processing applications, and are interesting because they allow operations from the continuous domain such as differentiation to be implemented in the discrete domain. An image matching algorithm illustrates the use of the properties, with improvements in computation time and matching quality.

傅立叶分解法荧光层析成像

本文提出一种基于结构光照明和傅立叶分解方法的荧光层析成像技术，该技术首先将激发光的强度沿着光轴方向调制成余弦函数，然后用此激发光对样品作传统的二维扫描，在每一个扫描位置余弦函数的频率在一定的范围内扫描，同时一一对应地记录下所发出的荧光强度。只要对所纪录的荧光序列做一个简单的傅立叶变换，即可以得到此位置样品沿着光轴方向的荧光团分布。这样通过一个传统的二维扫描，就可以得到一个三维的阳样品分布。

地形可视性分析中观察点设置问题研究

观察点设置问题是地形可视性分析中的一类重要问题，对该问题的研究可以在空间信息辅助决策、通信、旅游、野生动物保护等领域发挥重大作用。本文在对地形可视性分析中观察点设置问题现有研究成果总结和分析基础上对该问题展开深入研究。 首先，针对现有解决方法只从智能算法或地形数据表示方法单一角度进行分析和研究的局限性，提出了一种问题相关的智能算法和数据表示方法相结合的解决问题新框架。该框架考虑了解决观察点设置问题时智能算法的优点和数据表示方式的特点相互配合问题，目的是充分发挥二者各自的优势以提高观察点设置问题解决的准确度与效率。 其次，在深入分析观察点设置问题本身特点的基础上，结合隶属云理论的基本理论和方法，对经典模拟退火算法从退温函数设计、温度产生过程、状态生成过程三方面进行了问题相关的改进，提出了一种适于观察点设置问题的改进模拟退火算法(Improved Simulated Annealing algorithm, ISA)。该算法一方面保持了经典模拟退火算法的稳定倾向特性，保证了算法满足伴随退火温度的不断下降，对恶化的新状态越来越难于接受这一模拟退火算法的最基本特征；另一方面其退火温度的连续性随机变化特性和隐含的“回火升温”过程，则有利于算法有效拒绝恶化解，加速算法收敛，能够更好地满足观察点设置问题对于算法收敛速度的要求。 再次，在分析地形数据的精度、误差等因素对观察点设置问题的解决准确性和解决效率影响程度的基础上，提出了一种基于离散余弦变换的地形数据内插方法(Discrete Cosine Transformation Interpolation method, DCTI)。新方法将传统空域上的地形内插转换到变换域上进行，同时充分利用了离散余弦变换的熵保持特性和能量压缩特性，简化了变换域上的内插过程，提高了地形数据内插的效率和精度。DCTI方法与其他现有典型地形数据内插方法相比，对地形可视性信息获取的准确性和效率影响最小，为平衡观察点设置问题解决过程中时间效率和准确度之间的关系，最终有效地解决观察点设置问题提供了数据基础。 最后，从智能算法和地形数据相结合的角度出发，提出了一种基于ISA和DCTI相结合的观察点设置问题多分辨率处理方法(Multi-Resolution Processing method, MRP)。新方法将模拟退火算法的逐次退火特点和地形数据的多分辨率表示充分结合，达到了发挥算法数据相结合的综合优势的目的。与现有单纯基于模拟退火算法的解决方法相比，在问题解决准确度保持不变的前提下，基于MRP方法的观察点设置问题解决的平均耗时减少85%~95%，为实际工程应用问题的解决提供了一条重要途径。