Frequency domain

About: Frequency domain is a research topic. Over the lifetime, 53871 publications have been published within this topic receiving 701364 citations.

Fast Normalized Cross-Correlation

Abstract: Although it is well known that cross correlation can be efficiently implemented in the transform domain, the normalized form of cross correlation preferred for feature matching applications does not have a simple frequency domain expression. Normalized cross correlation has been computed in the spatial domain for this reason. This short paper shows that unnormalized cross correlation can be efficiently normalized using precomputing integrals of the image and image over the search window.

Computation of piecewise quadratic Lyapunov functions for hybrid systems

Abstract: This paper presents a computational approach to stability analysis of nonlinear and hybrid systems. The search for a piecewise quadratic Lyapunov function is formulated as a convex optimization problem in terms of linear matrix inequalities. The relation to frequency domain methods such as the circle and Popov criteria is explained. Several examples are included to demonstrate the flexibility and power of the approach.

Feature reduction and selection for EMG signal classification

Abstract: Feature extraction is a significant method to extract the useful information which is hidden in surface electromyography (EMG) signal and to remove the unwanted part and interferences. To be successful in classification of the EMG signal, selection of a feature vector ought to be carefully considered. However, numerous studies of the EMG signal classification have used a feature set that have contained a number of redundant features. In this study, most complete and up-to-date thirty-seven time domain and frequency domain features have been proposed to be studied their properties. The results, which were verified by scatter plot of features, statistical analysis and classifier, indicated that most time domain features are superfluity and redundancy. They can be grouped according to mathematical property and information into four main types: energy and complexity, frequency, prediction model, and time-dependence. On the other hand, all frequency domain features are calculated based on statistical parameters of EMG power spectral density. Its performance in class separability viewpoint is not suitable for EMG recognition system. Recommendation of features to avoid the usage of redundant features for classifier in EMG signal classification applications is also proposed in this study.

The analytic signal of two‐dimensional magnetic bodies with polygonal cross‐section: its properties and use for automated anomaly interpretation

Abstract: This paper presents a procedure to resoive magnetic anomalies due to two-dimensional structures. The method assumes that all causative bodies have uniform magnetization and a crosssection which can be represented by a polygon of either finite or infinite depth extent. The horizontal derivative of the field profile transforms the magnetization effect of these bodies of polygonal cross-section into the equivalent of thin magnetized sheets situated along the perimeter of the causative bodies A simple transformation in the frequency domain yields an analytic function whose real part is the horizontal derivative of the field profile and whose imaginary part is the vertical derivative of the field profile. The latter can also be recognized as the Hilbert transform of the former. The procedure yields a fast and accurate way of computing the vertical derivative from a given profile. For the case of a single sheet, the amplitude of the analytic function can be represented by a symmetrical function maximizing exactly over the top of the sheet. For the case of bodies with poiygonal cross-section, such symmetrical amplitude functions can be recognized over each corner of each polygon. Reduction to the pole, if desired, can be accomplished by a simple integration of the analytic function, without any cumbersome transformations. Narrow dikes and thin ilat sheets, of thickness less than depth, where the equivalent magnetic sheets are close together, are treated in the same fashion using the field intensity as input data, rather than the horizontal derivative. The method can be adapted straightforwardly for computer treatment. It is also shown that the analytic signal can be interpreted to represent a complex “field intensity,” derivable by differentiation from a complex “potential.” This function has simple poles at each polygon corner. Finally, the Fourier spectrum due to finite or infinite thin sheets and steps is given in the Appendix.