A common use of the z-transform is to solve difference equations.
76, which is defined in the context
77, solves
linear difference equations with constant coefficients:
<#3196#>
verbatim184#
<#3196#>
Here, we have asked for no justification (<#479#>Dialogue -;SPMgt; False<#479#>
and implied that the solution is right-sided since the default value
of the <#480#>RightSided<#480#> option is <#481#>True<#481#>.
Because the solution is assumed to be right-sided, the
<#482#>Step<#482#> term in the driving function is not necessary.
In this case, a full set of initial conditions is given.
In general, initial conditions are optional and the missing ones
are considered to be zero.
When solving a difference equation, <#483#>ZSolve<#483#> substitutes the
initial conditions into the left-hand side of the difference equation.
This gives rise to impulse functions on the right-hand side of the
difference equation that account for behavior before the driving function
turns on.
This approach enables the bilateral z-transform to solve the augmented
difference equation completely.