By Simon Haykin

ISBN-10: 0470069112

ISBN-13: 9780470069110

ISBN-10: 0470069120

ISBN-13: 9780470069127

ISBN-10: 0471735825

ISBN-13: 9780471735823

This collaborative paintings offers the result of over 20 years of pioneering examine by means of Professor Simon Haykin and his colleagues, facing using adaptive radar sign processing to account for the nonstationary nature of our environment. those effects have profound implications for defense-related sign processing and distant sensing. References are supplied in every one bankruptcy guiding the reader to the unique learn on which this booklet relies.

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3 The Integral Regression Single-Line F-Test Thomson [36] also suggests an integral regression test instead of the point regression at f0 that was developed above. 12 The single-line point regression F-test for NW = 2 and 4, applied to the Marple dataset. The corresponding F values for 99% and 95% confidence levels are drawn as well. 42) with respect to μ. The development is more complex now, but the underlying logic is the same as before. Again, we have an equivalent harmonic window, but here it is formed of convolutions of prolate functions that have exceedingly low sidelobes.

A brief outline of this test applied to linear regression models, is given in the following subsection; for more details, see Draper and Smith [7]. 1 Brief Outline of the F-Test Let us assume that we have a model described by y = Ax + e that is linear with respect to the p × 1 parameter vector x, where the n × p coefficient matrix A and n × 1 vector y are known or can be estimated from a given dataset. We assume that the error vector e has independent components that come from N(0,σ2). Therefore, another way to express our assumed model is to write E {y} = Ax In order to get the best possible estimate of our parameter vector x in the leastsquares sense, we have to find min y − Ax 2 x Using the superscript H to denote the Hermitian transposition of a matrix, we may express the squared error as e 2 ( x ) = e H e = y − Ax 2 = y H y − y H Ax − x H A H y + x H A H Ax which assumes its minimum value at the well-known linear least-squares solution −1 xˆ = ( A H A) A H y = A + y where A + = (AHA) −1AH is the pseudo-inverse of A.

First, we require that E {dZ ( f )} = 0 3 and second that the covariance function E {X (t1 ) X * (t2 )} = ∫ ∞ ∫ ∞ −∞ −∞ e j 2 πf1t1 − j 2 πf2 t2 E {dZ ( f1 ) dZ * ( f2 )} be a function of the time difference t1 − t2 only. 4) where S( f ) is the power spectral density of the process, representing the amount of power density at different frequencies. 3). Note also that at different frequencies, E{dZ(f1)dZ*(f2)} is zero; that is, the increments dZ( f ) are orthogonal (the energy at different frequencies is uncorrelated).

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Adaptive Radar Signal Processing by Simon Haykin

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