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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 two decades of pioneering study via 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 publication relies.

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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.

19) k =0 where the asterisk denotes complex conjugation. 20) n=0 We call the {xk ( f )} the eigencoefficients of the kth sample. 21) are, individually, the direct spectrum estimates, and we therefore call them eigenspectra. 22) k =0 The Adaptive Spectrum While the lower-order eigenspectra have excellent bias properties, there is some degradation as k increases toward 2NW. In his 1982 paper [36], Thomson introduces a set of weights {dk ( f )} that downweight the higher order eigenspectra. He derives 8 The name multiple-window or multi-taper is the result of using a multiplicity of windows in the spectrum estimation process instead of just one, as is commonly the practice.

3 Spectrum Estimation Background 15 periodogram). The Blackman and Tukey spectrum estimate, for a data sample of size N, is given by the formula N −1 Sˆ ( f ) = ∑ rˆ ( Δm ) d ( m ) e− j 2 πf Δm m =1− N where the autocorrelation sequence is estimated as rˆ ( Δm ) = 1 N −m ∑ x [Δ (n + m )] x* (Δn) N − m n =1 where 0 ≤ m ≤ N − 1, rˆ (Δm) = r*(−Δm) for m < 0, and Δ is the sampling period. The weight sequence {d(n)} has real positive elements satisfying d(m) = d(−m) to ensure that the spectral estimate is real, and d(0) = 1 to ensure that it is unbiased when the true spectrum is flat across B, where B = ( f : | f | < 1/2Δ}.

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Adaptive Radar Signal Processing by Simon Haykin

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