Linear Prediction is Peak SensitiveBy Rayleigh's energy theorem, (as shown in §2.3.8). Therefore,
From this ``ratio error'' expression in the frequency domain, we can see that contributions to the error are smallest when . Therefore, LP tends to overestimate peaks. LP cannot make arbitrarily large because is constrained to be monic and minimum-phase. It can be shown that the log-magnitude frequency response of every minimum-phase monic polynomial is zero-mean . Therefore, for each peak overestimation, there must be an equal-area ``valley underestimation'' (in a log-magnitude plot over the unit circle).
Linear Prediction Methods
Points to Note