Extending the Bandwidth of NarrowBand Speech Using Cepstral Linear Prediction
3. Linear Mapping Predictor
If we characterize the narrow band envelope by a vector of cepstral coefficients we call x = {x1, x2,……x8} we can predict the output highband envelope by a vector y = {y1,y2,y3,y4,….y16}through the following function:
y = Wx....................(2)
It should be noted however that W is trained prior to its use through matrices X and Y as matrices whose rows represent narrowband and highband vectors of generic speech signals respectively.
W, our predictor can thus be calculated by:
W = ( XTX)-1XTY....................(3)
We use a linear predictor based on prior training with generic speech files, to act as a multi-dimensional filter. This filer serves to map the 8 cepstral coefficients attained from 8 kHz speech to 16 cepstral coefficients which we use to model the 16 kHz speech at the enhancement stage.
The mesh plot of our predictor in Figure 1 is based on training of voiced segments across 20 speech files, excluding silence frames is shown below.
Figure 1: Linear prediction of Cepstral coefficients
The performance of our linear prediction for a particular voiced frame is featured in Figure 2. The deviations from the prediction and actual cepstral coefficients from the original 16 kHz speech file under test show good approximation.
Figure 2: Linear prediction of Cepstral coefficients
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