Rational Function Interpolation of Electromagnetic Transfer Functions of High-Speed Interconnect Systems from Discrete Time-Domain and Frequency-Domain Data

We present new methodologies to generate rational function approximations of broadband electromagnetic responses of linear and passive networks of high-speed interconnects, and to construct SPICE-compatible, equivalent circuit representations of the generated rational functions. These new methodologies are driven by the desire to improve the computational efficiency of the rational function fitting process, and to ensure enhanced accuracy of the generated rational function interpolation and its equivalent circuit representation. Toward this goal, we propose two new methodologies for rational function approximation of high-speed interconnect network responses. The first one relies on the use of both time-domain and frequency-domain data, obtained either through measurement or numerical simulation, to generate a rational function representation that extrapolates the input, early-time transient response data to late-time response while at the same time providing a means to both interpolate and extrapolate the used frequency-domain data. The aforementioned hybrid methodology can be considered as a generalization of the frequency-domain rational function fitting utilizing frequency-domain response data only, and the time-domain rational function fitting utilizing transient response data only. In this context, a guideline is proposed for estimating the order of the rational function approximation from transient data. The availability of such an estimate expedites the time-domain rational function fitting process. The second approach relies on the extraction of the delay associated with causal electromagnetic responses of interconnect systems to provide for a more stable rational function process utilizing a lower-order rational function interpolation. A distinctive feature of the proposed methodology is its utilization of scattering parameters. For both methodologies, the approach of fitting the electromagnetic network matrix one element at a time is applied. It is shown that, with regard to the computational cost of the rational function fitting process, such an element-by-element rational function fitting is more advantageous than full matrix fitting for systems with a large number of ports. Despite the disadvantage that different sets of poles are used in the rational function of different elements in the network matrix, such an approach provides for improved accuracy in the fitting of network matrices of systems characterized by both strongly coupled and weakly coupled ports. Finally, in order to provide a means for enforcing passivity in the adopted element-by-element rational function fitting approach, the methodology for passivity enforcement via quadratic programming is modified appropriately for this purpose and demonstrated in the context of element-by-element rational function fitting of the admittance matrix of an electromagnetic multiport.

Datasets, features, learning, and models in visual recognition

Visual recognition is a fundamental research topic in computer vision. This dissertation explores datasets, features, learning, and models used for visual recognition. In order to train visual models and evaluate different recognition algorithms, this dissertation develops an approach to collect object image datasets on web pages using an analysis of text around the image and of image appearance. This method exploits established online knowledge resources (Wikipedia pages for text; Flickr and Caltech data sets for images). The resources provide rich text and object appearance information. This dissertation describes results on two datasets. The first is Berg’s collection of 10 animal categories; on this dataset, we significantly outperform previous approaches. On an additional set of 5 categories, experimental results show the effectiveness of the method. Images are represented as features for visual recognition. This dissertation introduces a text-based image feature and demonstrates that it consistently improves performance on hard object classification problems. The feature is built using an auxiliary dataset of images annotated with tags, downloaded from the Internet. Image tags are noisy. The method obtains the text features of an unannotated image from the tags of its k-nearest neighbors in this auxiliary collection. A visual classifier presented with an object viewed under novel circumstances (say, a new viewing direction) must rely on its visual examples. This text feature may not change, because the auxiliary dataset likely contains a similar picture. While the tags associated with images are noisy, they are more stable when appearance changes. The performance of this feature is tested using PASCAL VOC 2006 and 2007 datasets. This feature performs well; it consistently improves the performance of visual object classifiers, and is particularly effective when the training dataset is small. With more and more collected training data, computational cost becomes a bottleneck, especially when training sophisticated classifiers such as kernelized SVM. This dissertation proposes a fast training algorithm called Stochastic Intersection Kernel Machine (SIKMA). This proposed training method will be useful for many vision problems, as it can produce a kernel classifier that is more accurate than a linear classifier, and can be trained on tens of thousands of examples in two minutes. It processes training examples one by one in a sequence, so memory cost is no longer the bottleneck to process large scale datasets. This dissertation applies this approach to train classifiers of Flickr groups with many group training examples. The resulting Flickr group prediction scores can be used to measure image similarity between two images. Experimental results on the Corel dataset and a PASCAL VOC dataset show the learned Flickr features perform better on image matching, retrieval, and classification than conventional visual features. Visual models are usually trained to best separate positive and negative training examples. However, when recognizing a large number of object categories, there may not be enough training examples for most objects, due to the intrinsic long-tailed distribution of objects in the real world. This dissertation proposes an approach to use comparative object similarity. The key insight is that, given a set of object categories which are similar and a set of categories which are dissimilar, a good object model should respond more strongly to examples from similar categories than to examples from dissimilar categories. This dissertation develops a regularized kernel machine algorithm to use this category dependent similarity regularization. Experiments on hundreds of categories show that our method can make significant improvement for categories with few or even no positive examples.