Digital Signal Processing Reference
In-Depth Information
power subject to the constraint that its response at the frequency of interest,
has unity gain. This constrained optimization is a key aspect of the MVDR
method that allows it to provide a lower bias with a smaller filter length than
the Periodogram method [41]. The Mth order MVDR spectrum can be
parametrically written as;
The parameters,
can be obtained using the linear prediction (LP)
coefficients,
and the prediction error variance
[41].
4.3.2
Direct Warping of FFT Spectrum
The aim of using a non-linearly spaced filterbank is to remove the
harmonic information that exists in voiced speech and smooth out the
spectrum. MVDR, on the other hand, can handle voiced speech by accurately
modeling spectral powers at the perceptually important harmonics. Therefore,
it is both
useful
and
safe
to remove the filterbank structure and incorporate the
perceptual considerations by directly warping the FFT spectrum. The warping
can be incorporated via a first order all pass system [42]. In fact, both Mel and
Bark scales can be implemented by changing only one system parameter,
We use the phase response of the first order system in Eq. (9) as the warping
function given in Eq. (10),
