ABSTRACT
This chapter develops an understanding of systems in terms of a special class of input signals called eigenfunctions. An eigenfunction of a system is an input signal which results in an output signal which is in the same form as the input signal. For signals which are eigenfunctions of a system, the shape of the output is identical to the shape of the input signal. The amplification or scaling factor of a system for an eigenfunction is given a special name, the eigenvalue. For each eigenfunction of a system there is an eigenvalue which gives the amount that the system amplifies the eigenfunction. In nuclear magnetic resonance spectroscopy, the response of a sample in an intense magnetic field to a radio frequency input is determined as a function of the frequency of the input signal. The frequency at which a nucleus in the sample responds to the input signal depends upon the chemical environment of a nucleus.
