Modeling, Estimation and Optimal Filtration in Signal Processing

Chapter 1

Parametric Models

1.1. Introduction

A “signal” corresponds to a physical quantity that varies with time, space, etc.

A wide range of parameters are converted to electrical signals. In an industrial process, for example, sensors allow the translation of parameters such as temperature, pressure, liquid and gas flow rates, etc., into electrical signals. The variation of the surrounding air pressure due to a person speaking through a microphone is translated into an electrical signal. Ground pressure variations can sometimes result from controlled events, such as in the case of artificial seismology when it is used for oil exploration. However, variations in ground pressure could also result from uncontrolled events such as earthquakes. In such a case, seismographs provide electrical signals to characterize the phenomenon.

Signals, the closest approximations of physical magnitudes, can be deterministic or random processes.

If the signals are deterministic, they can either be periodic or non-periodic, or combinations of periodic and random components. Their spectral content can be studied using transformations such as the Fourier transform. Such representations are said to be “non-parametric”, whether they are in the time or frequency domain. Their major advantage comes from the fact that they are easily exploitable.

However, the development of digital processors – their spread on the one hand and, on the other, the influence of identification methods developed for the analysis ...