Linear Systems and the Fourier Transform

In Chap. 1 we saw that an ultrasonic system has many components. Those components individually can be complex electromechanical systems such as, for example, the ultrasonic transducers. To model each of the elements that go into an ultrasonic system and how they work together to produce a measured response is a challenging task, indeed. In this chapter we will present a very general modeling framework of linear time-shift invariant (LTI) systems which we will use in order to describe a complete ultrasonic NDE measurement system. Many of the remaining chapters will fill in the details of this general framework and ultimately produce an explicit LTI models of the entire ultrasonic measurement process.