As a result, more precise estimates of spectral energy distribution are obtained.
To be more precise with the spectral clustering of each subshot defined above, let us denote the kth subshot as (phantom {dot {i}!}mathbf {X}_{k} = [x_{1},ldots,x_{3},ldots,x_{N_{k}}], ; k in {1,ldots,K}) where K is the number of subshots and N k is the size of X k.
Our ancestral reconstruction experiments allow for a more precise prediction of where spectral sensitivity shifts may have occurred, and provide an unusual example where descendants have re-evolved UVS from a violet type ancestor; the reverse being more common in most vertebrates.
Our results not only provide a more precise prediction of where these spectral sensitivity shifts occurred, but also confirm the hypothesis that birds are an unusual exception among vertebrates where some descendants re-evolved UVS from a violet type ancestor.
Our identification of VS type pigments in both passerine and parrot/passerine ancestors confirm this hypothesis, and our ancestral reconstruction results provide a more precise prediction of where these spectral sensitivity shifts occurred.
Nevertheless, the FFT-based spectral harmonics are an intermediate step in the computation of the envelope, so a more precise representation of the harmonics in relevant regions of the spectral envelope may help to get more accurate formant estimates and also more discriminative speech features.
Nevertheless, the system allows us to incorporate alternative high-resolution spectral estimation methods that might offer more precise information to the specialist.
We point out that the careful treatment of radiation pattern in spectral ratio calculation may lead to more precise estimation of site amplification factor.
Let (ngeq4), and it is easy to find that the upper bounds for the spectral norm of Theorem 2.8 are more precise than Theorem 1.5 (see Table 3).
It can be seen from Table 4 that the upper bounds for the spectral norm of Theorem 2.12 are more precise than Theorem 1.6 when (ngeq3).
