Applications to Linear Difference Equations

Applications to
Linear Difference
Equations

Outline
• Introduction
• Applications
• Properties
• Discrete time signals
• Linear Independence in
the space S of Signals
• Examples

Introduction
Difference Equations are often used to produce numerical solutions when
differential equations is used to model a continuous process.
Given scalars a0, ..., an, with a0 and an nonzero, and given a signal {zk}, the
equation
a0 yk+n + a1 yk+n-1 + + an-1 yk+1 + an yk = zk for all k (3)⋯
is called a linear difference equation (or linear recurrence relation) of order n. For
simplicity, a0 is often taken equal to 1.

Applications
• Difference Equations are used in a vector space
dealing with time (t) so the application is used
in digital signals that arise in electrical and
control systems: such as stop lights.