# CHAPTER *16*

# Extracting the Filter from a Waveform

Chapter 14 showed how all linear digital filters can be implemented as a combination of poles and zeros or, equivalently, as polynomials, in Equations 14.18 and 14.21. But we still don't know how to choose the poles and zeros necessary to reproduce a given waveform, such as the glockenspiel and piano waveforms shown in Chapter 13. This chapter develops one general-purpose technique and applies it to the glockenspiel and piano waveforms. The technique developed here is variously called *maximum entropy* or *linear predictive spectral estimation*.

## 16.1 GENERAL LINEAR PREDICTIVE ESTIMATION

While the “maximum entropy” terminology has a certain appeal for theoretical reasons (at least if you are familiar with information theory), I prefer the “linear predictive” (LP) terminology, because it better describes the process. Linear predictive coding (LPC) is a technique used for signal compression. Linear predictive spectral estimation, explored in this chapter, is a nonlinear spectral estimation technique. In both cases the basic LP process is used to estimate a filter that could have produced the observed waveform given some assumed driving force. Thus, the more fundamental technique might be called linear predictive filter estimation.

You may be familiar with terms such as LPC-10, which is used for speech compression and means that a 10-coefficient version of linear predictive coding is used to compress speech waveforms. The idea is to estimate ...