#### Linear Prediction is Peak Sensitive

By 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*[162]. Therefore, for each peak overestimation, there must be an equal-area ``valley underestimation'' (in a log-magnitude plot over the unit circle).

**Next Section:**

Linear Prediction Methods

**Previous Section:**

Points to Note