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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 environment. those effects have profound implications for defense-related sign processing and distant sensing. References are supplied in each one bankruptcy guiding the reader to the unique learn on which this booklet is predicated.

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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. These operators do not commute, that is, PTPF ≠ PFPT.

The fact that more than one window is used makes for a smaller variance in the estimator. Also, since the signal power concentration within the analysis band is large (eigenvalues close to one), the bias introduced from the multiplicity of windows is kept small. 5 TEST DATASET AND A COMPARISON OF SOME POPULAR SPECTRUM ESTIMATION PROCEDURES In order to check our understanding of the multi-taper method, at each stage of the development, we try to implement it on a known test dataset. This set consists of a complex time series of N = 64 points as described in reference 22.

3) (modified 2 Generalization of the treatment to more dimensions is done by simply allowing time t to become a d-dimensional vector t, where d is the dimension of the process. See references 5 and 6 for a concise explanation. In the following, we consider one-dimensional processes only, since they adequately describe our experimental data. 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.

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