By Simon Haykin
This collaborative paintings offers the result of over 20 years of pioneering study by way 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 each one bankruptcy guiding the reader to the unique learn on which this publication is predicated.
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Extra info for Adaptive Radar Signal Processing
The connection with Slepian’s original exposition  is established by writing Vk ( f ) = (1 ε k ) e − jπf ( N −1)U k ( − f ) 7 Thomson  uses the routines BISECT and TINVIT to evaluate the Slepian sequences, and λk (N, W ) = W 12 ∫−W Vk ( f ) 2 df ∫−1 2 Vk ( f ) 2 df for the eigenvalues. Inclusion of N in the argument arises due to dependence of V k ( f) on N. 17) n=0 A step-by-step procedure involved in computing the data υ(k) n ’s and spectral V k ( f )’s windows (Slepian sequences and functions) is summarized as follows: 1.
Basically, Thomson has proved that a more fruitful approach to a spectrum estimator is through the spectral representation of X(t) itself (Cramér representation). Ishimaru  gives a particularly lucid explanation of how this representation is deﬁned. 1). In attempting to develop a spectral representation for the random function X(t), it is tempting to write down the Fourier transform X (t ) = ∫ ∞ −∞ X ( f ) e j 2πft df However, the stationarity assumption is then violated, since Dirichlet’s condition requires that X(t) be absolutely integrable—that is, that ͐∞−∞|X(t)| dt be ﬁnite.
Actually, another way of viewing MTM, is by having the data pass through the baseband (low-pass) ﬁlter (Fig. 4) as it slides over all frequencies in the interval (−1/2, 1/2). Since spectrum estimation is essentially the estimation of signal power within a certain analysis window and this can ideally be done with a narrow rectangular ﬁlter, we see that the baseband ﬁlter is the best possible approximation of such a window. The fact that more than one window is used makes for a smaller variance in the estimator.