# LTI Systems

Consider the 1-dimensional system given by: ∀
*n *∈
*Naturals*_{0}
,

*s*(*n* + 1) = *as*(*n*) + *bx*(*n*)

*y*(*n*) = *cs*(*n*) + *dx*(*n*)

where *a*, *b*, *c*, *d* are fixed real-valued constants.
This is a particularly simple form of the *nextState* and *output*
functions.
A system of this form is called a **linear, constant-coefficient difference
equation (LCCDE) system**.

If the initial state is zero, *s*(0) = 0, and if we interpret the index
*n* to represent (discrete) time, then it is also called a **linear time-invariant
(LTI) system.**