The following graphs show in orange two LPC spectral envelopes of the same vowel.
A. ![[order20.png]]
B.![[lpc24.png]]
Which of the spectral envelopes was computed with a higher LPC order?
> [!Solution]-
> The second graph (B) shows more resonances in the LPC spectral envelope (in orange) meaning that it was computed with a higher LPC order. The [[linear prediction]] all-pole filter can be seen as similar to the vocal tract transfer function. The spectral envelope is the magnitude of the [[frequency response]] of the all-pole LPC filter:
> $
> |H(e^{j\omega})|_{dB} = 20 \log \left|\frac{1}{1-\sum_{k=1}^{P}a_{k}e^{-j\omega k}} \right|
> $
> where $a_{k}$ are the [[linear prediction coefficients]] and $P$ is the LPC order. A higher value of $P$ results in a larger number of [[poles of the transfer function]] that provide a more detailed modeling of the spectral envelope of the signal.