Abstruct-In many areas the time delay of arrival (TDOA) is desired. In the case of narrowband signals we propose a fast and simple method to estimate small time delays. This method is shown to have the same or better accuracy as the cross correlation methods for small delays in the order of fractions of the sample interval. It is based on using the Hilbert transform in correlation between two signals and consists of only one scalar product, which makes it fast. It may also be used in applications with narrowband signals where the measurements are repeatable, such as ultrasonic imaging and nondestructive testing. In ultrasonic applications, due to fluctuations in the insonified media, a small random time shift may be present causing the signals to be misaligned in time. Averaging signals under these conditions will result in a distortion of the signal shape. We propose an averaging method to avoid this and to accomplish a higher SNR without the distortion. Simulations and experiments from ultrasonic applications are presented.

In this paper we present a general strategy for screening discrete variations in organic synthesis. The strategy is based upon principal properties, i.e. principal component characterization of the constituents defining the reaction system. The first step is to select subsets of test items from each class of constituents defining the reaction space, i.e. substrates, reagents, solvents, catalysts, etc., so that the selected items from each class cover the properties considered. The second step is to construct a candidate matrix which contains all possible combinations of the items in the subsets. This matrix is a full multilevel factorial design. The third step is to assign a tentative model for the screening experiment and to construct the corresponding candidate model matrix. The fourth step is to select experiments to yield an experimental design that spans the variable space efficiently and that also gives good estimates of the model parameters. We present an algorithm that uses singular value decomposition to select experiments. The proposed strategy is then illustrated with an example of the Fischer indole synthesis.

SUMMARYIn this paper we present a general strategy for screening discrete variations in organic synthesis. The strategy is based upon principal properties, i.e. principal component characterization of the constituents defining the reaction system. The first step is to select subsets of test items from each class of constituents defining the reaction space, i.e. substrates, reagents, solvents, catalysts, etc., so that the selected items from each class cover the properties considered. The second step is to construct a candidate matrix which contains all possible combinations of the items in the subsets. This matrix is a full multilevel factorial design. The third step is to assign a tentative model for the screening experiment and to construct the corresponding candidate model matrix. The fourth step is to select experiments to yield an experimental design that spans the variable space efficiently and that also gives good estimates of the model parameters. We present an algorithm that uses singular value decomposition to select experiments. The proposed strategy is then illustrated with an example of the Fischer indole synthesis.

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