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Download Adaptive Radar Signal Processing by Simon Haykin PDF

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By Simon Haykin

This collaborative paintings provides the result of over two decades of pioneering examine 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 every one bankruptcy guiding the reader to the unique study on which this publication relies.

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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. To 16 Chapter 2 Angle-of-Arrival Estimation in the Presence of Multipath avoid this difficulty, the random function is represented by a stochastic Fourier– Stieltjes integral, as shown by X (t ) = ∫ ∞ e j 2πft dZ ( f ) −∞ where dZ( f ) is called the random amplitude or increment process.

Each filter has the identical raised cosine response, seen in Fig. 5 The eigenvalue spectrum for NW = 4 and N = 64. As we can see, the first 8 eigenvalues are very close to 1, corresponding to the first K = 2NW = 8 windows that have a negligible effect on the bias of the spectrum estimator. 6 The exact known analytic spectrum of Marple’s synthetic dataset. 35. The maximum power level of this noise process is 15 dB lower than the doublet and 5 dB higher than the singlets. Note that even though the shape of the colored noise process is identical in the exact, analytic form of the spectrum for both positive and negative frequencies, this 26 Chapter 2 Angle-of-Arrival Estimation in the Presence of Multipath symmetry is not expected to be seen in the estimated spectrum because the real and imaginary components were generated independently.

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}. The modified periodogram spectrum estimate is given by Sˆ ( f ) = 2 N ∑ x (Δn) c (n) e − j 2 πf Δn n =1 where f ∈ B and the weight sequence {c(n)} typically has real, positive elements satisfying ΣNn=1c2 (n) = Δ to ensure that the spectral estimator is unbiased when the true spectral density is flat across B.

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