Autocorrelation method

Laroche, 1993] Laroche, J. (1993). Autocorrelation method for high quality time/pitch scaling. In Proc. IEEE Workshop Appl. of Signal Processing to Audio and Acoustics, Mohonk Mountain House, New Paltz, NY. 

Using this expression enables us to make use of the fast Fourier transform algorithms, which provide an enormous gain in speed over the equivalent autocorrelation method of equation (29). 

Zakarya, D., Belkhadir, M. and Fkih-Tetouani, S. (1993a). Quantitative Stmcture-Biodegradabil-ity Relationships (QSBRs) Using Modified Autocorrelation Method (MAM). SAR QSAR... 

Zakarya, D., Tiyal, F. and Chastrette, M. (1993b). Use of the Multifunctional Autocorrelation Method to Estimate Molar Volumes of Alkanes and Oxygenated Compounds Comparison Between Components of Autocorrelation Vectors and Topological Indexes. J.Phys.Org.Chem., 6,574-582. 

Nohair, M. and Zakarya, D. (2003) Prediction of solubility of aliphatic alcohols using the restricted components of autocorrelation method (RCAM). /. Mol. Model, 9, 365-371. 

Nohair, M., Zakarya, D. and Berrada, A. (2002) Autocorrelation method adapted to generate new atomic environments application for the prediction of 13-C chemical shifts of alkanes. 

To avoid the issue of alignments in 3D-QSAR, several autocorrelation methods have been proposed by the groups of Broto et al. [101], Wagener et al. [102], and Clementi et al. [103]. Except for Broto et al. s method (used on 2-D or 3-D structures), these methods require a 3-D molecular structure, i.e., they are based on the choice of a conformer. The ALMOND program [25], built on initial work from Clementi et al. [103], is described below because of its convenient use of graphical outputs that relate autocorrelation vectors to MIFs, as well as to molecular structures. 

In analog detection methods (See Section 4.B.2) the photomultiplier output is treated as a continuous variable. At low light-scattering levels, the signal-to-noise ratio in these methods may become small because of various sources of ftostdetection noise in the system (thermal or Johnson noise, PM dark current, etc.). Under these conditions it becomes advantageous to use the digital or photocount autocorrelation method. 

A slightly different method know as the autocorrelation method can also be used, and as this has many practical advantages over the covariance method, it is often the method most used in practice. 

In many cases, especially in female or other high pitched speech, the length of the closed phase can be very small, perhaps only 20 or 30 samples. In the autocorrelation method, the initial samples of the residual are dominated by the errors caused by calculating the residual from the zero signal before the window. The high (and erratic) error in the residual can be seen in the first few samples of the residual in Figure 12.17b. For short analysis windows this can lead to a residual dominated by these terms, and for this reason, covariance analysis is most commonly adopted for closed phase analysis. 

The FROG method provides information on the time-dependent frequency spectrum of a short pulse but cannot measure the phases of these spectral components. A newly developed technique is helpful in this case this method is called SPIDER (Spectral Phase /nterferometry for Direct Field Reconstruction). It uses the interference structure generated when two spatially separated pulses are superimposed [788]. Similar to the autocorrelation method, the two pulses are generated from the input pulse that is to be measured, using a beam splitter and a delay line which changes the time delay between the two pulses. The second pulse is therefore a copy of the first pulse with a time delay t. The electric field amplitude... 

In contrast, once well-defined clusters or precipitates have formed (see, for example. Fig. 9.18a), one can use more readily-accessible parameters such as precipitate size, composition and number density. However, defining these parameters is rather more complex than one might imagine. Many methods have been used, including simple sampling, Fourier and autocorrelation methods. However, the most successful are based on the simple premise that the clusters are enriched in solute relative to the matrix and therefore the solute atoms are closer together in clusters than they are in the matrix. This will be true provided that the density of atoms in the reconstructed volume is approximately uniform. Thus the approach taken is to search for regions enriched in solute atoms as outlined in Fig. 9.19. The process is called the maximum separation method and involves ... 

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