The spectral representation is the natural way a spectral envelope was presented in the previous chapters: as an amplitude curve in the frequency-domain, based on an equidistant or logarithmically spaced frequency grid. Each of the n grid point is also called a frequency bin . This representation is also called sampled spectral envelope representation, because we take a sample of the value of the (theoretically) continuous curve at each point of the frequency grid.
This representation is as stable as the filter coefficients, because it is derived directly from them. It is local, and when the frequency scale is linear, it is orthogonal, because the amplitude at each frequency can be changed independently from the others.
It is the most flexible representation (due to the high locality), but not that easy to manipulate, because the locality demands that all the values at all the frequencies be given. Especially when we think of an application for the singing voice, the preferred manipulations are changes of the position and bandwidth of formants, which means that new amplitude values would have to be specified for the whole frequency range of the spectral envelope the formant occupies.
They are fastest for additive synthesis and reasonably fast for filtering. They are reasonably compact, since the space required can be as low as 100 points, even less when a logarithmic frequency scale is used.5.1 Manual input is easy.