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By Simon Haykin

This collaborative paintings offers the result of over 20 years of pioneering study by means 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 learn on which this e-book relies.

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Example text

The corresponding F values for 99% and 95% confidence levels are drawn as well. 42) with respect to μ. The development is more complex now, but the underlying logic is the same as before. Again, we have an equivalent harmonic window, but here it is formed of convolutions of prolate functions that have exceedingly low sidelobes. The drawback is that as it uses information from a wider bandwidth, it is therefore subject to noise from the same bandwidth. 46) n=0 k =0 14 In his more recent work [38], Thomson discusses the F-tests, both single and multiple, in some detail.

It is helpful here to think of the energy in the band( f − W, f + W) as a signal component and the energy outside it as a noise component. 23) is then simply a process of finding the optimum Wiener filter. 26) is just the energy of the Slepian function in the outer band with value(1 − λk). The second one, by filling the tap in the inner band, has as expected value the average power of the process, σ2 (the process variance). 27) 9 Though unobservable, the exact coefficients of the expansion are important in the sense that they are the expansion coefficients which would be obtained if the entire process were passed through an ideal bandpass filter from ( f − W) to ( f + W) before truncation to the finite-sample size.

This makes it impossible to find exact or unique solutions. Instead, our goal becomes one of searching for approximate solutions whose statistical properties are, in some sense, close to those of dZ( f ). The above observation is another way of saying that the problem of spectrum estimation from finite data is an ill-posed inverse problem. Mullis and Scharf [25] define both the time-limiting operation (windowing, finite data) and isolation in frequency (power in a finite spectral window) as projection operators on the data, PT and PF, respectively.

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