ABSTRACT
This chapter discusses the linear shift-invariant system and its fundamental mathematical concepts and describes mathematical treatments. The shift-invariant property for the space coordinate of x means that the characteristic of the system S is not changed and the shape of the output is not changed, but the position is changed depending on the position of the input. The shift-invariant system in time is sometimes called a stationary system or a time-invariant system. In many cases, when we analyze scientific and engineering systems as well as optical systems, we use the method in which characteristics of a system are estimated or evaluated by the relation between its input and output. The output of the impulse input is called the impulse response. It is amazing that all the characteristics of the linear shift-invariant system are described by the impulse response.
