33 see problem 918 for details we see that the pole

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spectrum of a PZ(12, 6) model using the least-squares algorithm described in Section 9.3.3 (see Problem 9.18 for details). We see that the pole-zero model matches zeros ( valleys ) in the periodogram of the data better than other models do. 9.5 MINIMUM-VARIANCE SPECTRUM ESTIMATION Spectral estimation methods were discussed in Chapter 5 that are based on the discrete Fourier transform (DFT) and are data-independent; that is, the processing does not depend on the actual values of the samples to be analyzed. Window functions can be employed to cut down on sidelobe leakage, at the expense of resolution. These methods have, as a rule of thumb, an approximate resolution of f 1 /N cycles per sampling interval. Thus, for all these methods, resolution performance is limited by the number of available data samples N . This problem is only accentuated when the data must be subdivided into segments to reduce the variance of the spectrum estimate by averaging periodograms. The effective resolution is then on the order of 1 /M, where M is the window length of the segments. For many applications the amount of data available for spectrum estimation may be limited Manolakis, Dimitris, et al. Statistical and Adaptive Signal Processing : Spectral Estimation, Signal Modeling, Adaptive Filtering and Array Processing, Artech House, 2005. ProQuest Ebook Central, . Created from southernmethodist on 2017-10-18 10:27:14. Copyright © 2005. Artech House. All rights reserved.

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472 chapter 9 Signal Modeling and Parametric Spectral Estimation 0 5 10 15 20 25 30 1 0 1 Time (ms) ( a ) 0 1 2 3 4 5 20 10 0 10 20 30 40 50 60 Frequency (kHz) ( b ) Power (dB) Periodogram AP (16) PZ (12, 6) FIGURE 9.18 ( a ) Speech segment and ( b ) periodogram, spectrum of a data windowing-based AP(16) model, and spectrum of a residual windowing-based PZ(12, 6) model. either because the signal may only be considered stationary over limited intervals of time or may only be collected over a short fi nite interval. Many times, it may be necessary to resolve spectral peaks that are spaced closer than the 1 /M limit imposed by the amount of data available. All the DFT-based methods use a predetermined, fi xed processing that is independent of the values of the data. However, there are methods, termed data-adaptive spectrum estimation (Lacoss 1971), that can exploit ac- tual characteristics of the data to offer signi fi cant improvements over the data-independent, DFT-based methods, particularly in the case of limited data samples. Minimum-variance spectral estimation is one such technique (Capon 1969). Like the methods from Chapter 5, the minimum-variance spectral estimator is nonparametric; that is, it does not assume an underlying model for the data. However, the spectral estimator adapts itself to the character- istics of the data in order to reject as much out-of-band energy, that is, leakage, as possible.
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