Experimental Setup

We used a data size of $N=256$ in our simulations. The MFCC spectral model we used is specified by (11.5), where ${\bf b}$ is given in table 11.1 and the columns of ${\bf A}$ are the MEL band functions (Hanning-shaped MEL band functions calculated for a sample rate of 16000 Hz).

Table 11.1: Coefficients that define the MFCC-like model used in the simulations.

Coef	Value	Coef	Value
$b_1$	6.940937	$b_5$	21.734748
$b_2$	7.371341	$b_6$	140.720039
$b_3$	7.981074	$b_7$	47.916180
$b_4$	10.167393	$b_8$	8.350037

To make the simulations more “interesting", we made the AR and MFCC model spectra as similar as possible by approximating the MFCC power spectrum with an AR model. Thus, we created the AR model by inverting the MEL cepstrum to obtain the ACF, then used the Levinson algorithm to obtain the following AR(2) model $a_1 = -0.04101841,$ $a_2= -0.55743570$. These coefficients were used to create the circular AR models (11.4). The AR and MFCC-like spectra are plotted in Figure 11.1, which also shows the sample mean power spectra from 1000 samples of each model.

Figure 11.1: Power spectra, theoretical (smooth curves) and estimated (symbols). Circles: AR, Triangles: MFCC. Both spectra produce the same AR features.