Advantages over other representations

Eqn. (1) has the advantage over other commonly used equations of the van der Waal s type of giving an improved representation of the vapour pressure and molar liquid volume. 

A similar description has been employed by Leckie and Onat [17] and Onat and Leckie [18] and Onat [19] to include damaged-induced microstructural anisotropy into constitutive equations. Despite its advantages over other forms of representation, this approach has not been applied widely to the description of anisotropic microstructures and its inclusion in constitutive laws for materials. 

Propagators have the advantage of giving direct information about transition energies and amplitudes from a reference state, but like density matrices, they suffer from a lack of simple ways generally to ensure so-called A-representability or correspondence to proper many-electron state vectors. Nevertheless, the propagator approach to semi-empirical many-electron theory appears to have certain advantages over other methods. Such treatment has led to useful relations between matrix elements in the PPP-model P... 

Modification is performed by separating the harmonics from the spectral envelope, but this is achieved in a way that doesn t perform explicit source/filter separation as with LP analysis. The spectral envelope can be found by a number of numerical techniques. For example, Kain [244] transforms the spectra into a power spectrum and then uses an inverse Fourier transform to find the time domain autocorrelation function. LP analysis is performed on this to give an allpole representation of the spectral envelope. This has a number of advantages over standard LP analysis in that the power spectrum can be weighted so as to emphasise the perceptually important parts of the spectrum. Other techniques use peak picking in the spectrum to determine the spectral envelope. Once the envelope has been found, the harmonics can be moved in the frequency domain and new amplitudes found from the envelope. From this, the standard synthesis algorithm can be used to generate waveforms. 

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