By Simon Haykin
This collaborative paintings provides the result of over 20 years of pioneering examine via 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 ebook relies.
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Additional resources 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.
The ﬁrst pair is consistent with our model and has a larger F value, so it is the one we pick. The advantage with this particular representation is that we can project the maximum of F(f, Δ f) onto the f-axis and resolve the doublet from a simpler, onedimensional function. Note, however, the appearance of spurious peaks, particularly near the edges of the window boundary. These are explained by the fact that the sliding window (Fig. 4) is not an ideal bandpass ﬁlter; hence, energy from outside the window, particularly near the window boundaries, can affect the estimation inside the window.
3 The ﬁrst four spectral windows for the case N = 64 and NW = 4. 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.
Adaptive Radar Signal Processing by Simon Haykin