Spectral estimators

Burshtein A. I., McConnell J. Spectral estimation of finite collision times in liquid solutions, Physica A157, 933-54 (1989). 

In 1983, Sasaki et al. obtained rough first approximations of the mid-infrared spectra of o-xylene, p-xylene and m-xylene from multi-component mixtures using entropy minimization [83-85] However, in order to do so, an a priori estimate of the number S of observable species present was again needed. The basic idea behind the approach was (i) the determination of the basis functions/eigenvectors V,xv associated with the data (three solutions were prepared) and (ii) the transformation of basis vectors into pure component spectral estimates by determining the elements of a transformation matrix TsXs- The simplex optimization method was used to optimize the nine elements of Tixi to achieve entropy minimization, and the normalized second derivative of the spectra was used as a measure of the probability distribution. 

Figure 4.6 Pure component spectral estimates of Co2(CO)g and Co4(CO)i2 obtained from the local minimum of the fourth derivative, unweighted, full-spectrum minimizations. (Y Pan,...

These techniques are also often referred to as "spectral subtraction . We will not use this terminology in order to avoid ambiguities between the general principle and the particular technique described in [Boll, 1979], nor will we use the term spectral estimation as quite a number of the STSA techniques are not based on a statistical estimation approach. 

Evans et al., 1981] Evans, J., Johnson, J., and Sun, D. (1981). High resolution angular spectrum estimation techniques for terrain scattering analysis and angle of arrival estimation. Proc. IstASSP Workshop on Spectral Estimation, pages 5.3.1-5.3.10. 

Fritts, D.C., and W. Lu, Spectral estimates of gravity wave energy and momentum fluxes, II. Parameterization of wave forcing and variability. J Atmos Sci 50, 3695, 1993. 

As discussed in Sec. 12.3.1, we constructed the class of nonstationary Gaussian processes such, that they become locally stationary for small scales (see Eq. (12.8)). Hence, when the averaging kernel A(.) is adapted to the process variability on each scale, it includes more and more reproducing kernels, such that the variance of the spectral estimate vanishes in the limit of small scales. Then, the following relation for the variance Far a (a) of the averaged wavelet spectral estimate holds ... 

Estimate the (1 — a)-quantile Scrit (i-e. the critical value) of the corresponding background spectrum by Monte Carlo simulations. Depending on the chosen background model and the chosen normalization of the spectral estimator, the critical value in general depends on scale. 

Muller, E., Nobach, H. and Tropea, C., LDA signal reconstruction Application to moment and spectral estimation. 7th Int. Symp. on Appl. of Laser Techniques to Fluid Mechanics, Lisbon, Portugal, Paper 23.2 (1994)... 

At 290 and 594 m depths at the west of Yonakuni Island, the Kuroshio was quite steady dming the period of May 18 to June 1. The rotary spectral estimates of the cmrent data, by the maximmn entropy method, showed that there were peaks with the periods from 3 to 7 d. There is a significant coherence between the time series of cmrents at 290 and 594 m depths in the range from 3 to 5 d. 

In our estimation of the baseline and ptunp cycle, we must exclude the sulfate peak. To specify the computations, we define a weight fimction w(t). This weight function includes the cosine-bell tapering of the ends of the Intervals needed to reduce the bias in spectral estimation (2). Let the Interval to be excluded because it has the sulfate peak be denoted by [tj, t, ]. We let... 

Standard cepstral analysis can be used for a number of purposes, for example FO extraction and spectral envelope determination. One of the main reasons that cepstral coefficients are used for spectral representations is that they are robust and well suited to statistical analysis because the coefficients are to a large extent statistically independent. In synthesis however, measuring the spectral envelope accurately is a critical to good quality and many teclmiques have been proposed for more accurate spectral estimation than classic linear prediction or cepstral analysis. 

One ofthe most widely used techniques is the STRAIGHT set of analysis tools [ ].This system is operates as high quality speech analysis-modification-synthesis method implemented as a channel vocoder and has separate components for instantaneous-ffequency-based FO extraction and pitch-adaptive spectral smoothing. STRAIGHT attempts to obtain a more accurate spectral estimation and a use more sophisticated soiuce model than simple impulses. A comparison of STRAIGHT and standard cepstral analysis is showen in Figure 15.17. 

Wang, Y.Y. Xu, J.W He, L. 2011. Computational analysis of wave spectral estimation. Journal of Harbin Engineering University 32 (10) 1283-1289. 

Bluestein, D., and Einav, S., Spectral estimation and analysis of LDA data in pulsatile fiow through heart valves, Experiments in Fluids, 15 341-353, 1993. 

This representation can also be seen as a system model in which the given biosignal is assumed to be the output of a linear time-invariant system that is driven by a white noise input e(/t). The coefficients or parameters of the AR model a, become the coefficients of the denominator polynomial in the transfer function of the system and therefore determine the locations of the poles of the system model. As long as the biosignal is stationary, the estimated model coefficients can be used to reconstruct any length of the signal sequence. Theoretically, therefore, power spectral estimates of any desired resolution can be obtained. The three main steps in this method are... 

It is critical to estimate the right model order because this determines the number of poles in the model transfer function (between the white noise input and the signal output). If the model order is too small, then the power spectral estimate tends to be biased more toward the dominant peaks in the power spectrum. If the model order is larger than required, it often gives rise to spurious peaks in the power spectral estimate of the signal. 

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