Search

The covariance function and the variogram play very important roles in modelling and in prediction of spatial and spatio-temporal data. The assumption of second order stationarity, in space and time, is often made in the analysis of spatial data and the spatio-temporal data. Several times the assumption of stationarity is considered to be very restrictive, and therefore, a weaker assumption that the data is Intrinsically stationary both in space and time is often made and used, mainly by the geo-statisticians and other environmental scientists. In this paper we consider the data to be intrinsically stationary. Because of the inclusion of time dimension,the estimation and derivation of the sampling properties of various estimators related to spatio-temporal data become complicated. In this paper our object is to present an alternative way, based on Frequency Domain methods for modelling the data. Here we consider Discrete Fourier Transforms (DFT) defined for the (Intrinsic) time series data observed at several locations as our data, and then consider the estimation of the parameters of spatio-temporal covariance function, estimation of Frequency Variogram, tests of independence etc. We use the well known property that the Discrete Fourier Transforms of stationary time series evaluated at distinct Fourier Frequencies are asymptotically independent and distributed as complex normal in deriving many results considered in this paper., Comment: 25 pages

We consider a stationary spatio-temporal random process and assume that we have a sample. By defining a sequence of discrete Fourier transforms at canonical frequencies at each location, and using these complex valued random varables as observed sample, we obtain expressions for the spatio-temporal covariance functions and the spectral density functions of the spatio-temporal random processes. These spectra correspond to non separable class of random processes. The spatio-temporal covariance functions, obtained here are functions of the spatial distance and the temporal frequency and are similar to Matern class. These are in terms of modified Bessel functions of the second kind. and the parameters are in terms of the second order spectral density functions of the random proces and the spatial distances. We consider the estimation of the parameters of the covariance function and also briefly mention their asymptotic properties. The estimation of the entire data at a known location, and also the estimation of a value given the above sample is also considered. The predictors are obtained using the vectors of Discrete Fourier Transforms. We also describe a statistical test for testing the independence of the m spatial time series (testing for spatial independence) using the Finite Fourier Transforms and it is based on the likelihood ratio test of complex valued random variables The methods are illustrated with real data. Keywords: Discrete Fourier Transforms, Covariance functions, Spectral density functions, Space-Time Processses, Prediction(kriging) Laplacian operators, Frequency Variogram, Tests for independence, Whittle likelihood., Comment: 29 pages 5 figures

In this paper a low power and low area array multiplier with carry save adder is proposed. The proposed adder eliminates the final addition stage of the multiplier than the conventional parallel array multiplier. The conventional and proposed multiplier both are synthesized with 16-T full adder. Among Transmission Gate, Transmission Function Adder, 14-T, 16-T full adder shows energy efficiency. In the proposed 4x4 multiplier to add carry bits with out using Ripple Carry Adder (RCA) in the final stage, the carries given to the input of the next left column input. Due to this the proposed multiplier shows 56 less transistor count, then cause trade off in power and area. The proposed multiplier has shown 13.91% less power, 34.09% more speed and 59.91% less energy consumption for TSMC 0.18nm technology at a supply voltage 2.0V than the conventional multiplier., Comment: 5 pages, 6 figures; IJCSI International Journal of Computer Science Issues, Vol. 8, Issue 3, No. 2, May 2011