Transforms

 

The first step in data analysis is to learn how to represent and manipulate waveforms in a digital computer. Time and space are ordinarily regarded as continuous, but for purposes of computer analysis we must discretize them. This discretizing is also called digitizing or sampling. Discretizing continuous functions may at first be regarded as an evil that is necessary only because our data are not always known analytic functions. However, after gaining some experience with sampled functions, one realizes that many mathematical concepts are easier with sampled time than with continuous time. For example, in this chapter, the concept of the Z transform is introduced and is shown to be equivalent to the Fourier transform. The Z transform is readily understood on a basis of elementary algebra, whereas the Fourier transform requires substantial experience in calculus.