By Simon Haykin
This collaborative paintings provides the result of over two decades 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 surroundings. 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 examine on which this booklet relies.
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Extra info for Adaptive Radar Signal Processing
Even though the eigenvalues θk are not equal to λk, they are ordered in the same way and the eigenvectors are the same. Tridiagonal systems are easier than Toeplitz to solve, and this offers a practical way of numerically computing the eigenvectors. In actuality, only a small number of eigenvalues and eigenvectors is needed. 16) ∫−W Dn( f − ν)Vk ( ν)d ν = λ kVk ( f ) where, for notational simplicity, the dependence on N and W has been suppressed. 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.
K υ(nk ) x ( n ) e − j 2 πnf1 f1 −W n=0 k =0 K −1 N −1 N −1 f1 +W c2 df = . . 47). We just have to set f0 = f1. 60) tests the existence of two lines only. If again, we let f1 vary over the entire frequency range, f2 will vary in (f1 − W, f1 + W). As we can see from Figs. 19 for NW = 2, the doublet is resolved and the spurious peak problem disappears. 20 shows the corresponding result for NW = 4. 6 Line Component Extraction The next step in the spectrum estimation procedure is to extract the line components in order to be left with only the continuous part of the spectrum under investigation.
These are the complex amplitudes squared (in dB) of the Fourier transforms of the above data windows. optimum in the sense of energy concentration within the frequency band ( f − W, f + W). In essence, by using them, we are maximizing the signal energy within the band ( f − W, f + W) and minimizing, at the same time, the energy leakage outside this band. They are therefore the ideal choice to use as a basis of expansion in the frequency domain for band-limited processes. Actually, another way of viewing MTM, is by having the data pass through the baseband (low-pass) ﬁlter (Fig.
Adaptive Radar Signal Processing by Simon Haykin