2.12  Nonhomogeneous Difference Equations and Their Solutions

The solution of the nonhomogeneous difference equation

y(n)k=1Naky(nk)=k=0Mbxx(nk)

can be obtained by finding the homogeneous solution of

y(n)k=1Naky(nk)=0

with the initial conditions

y(1),y(2),,y(N)

then adding it to the particular solution of

y(n)k=1Naky(nk)=k=0Mbxx(nk)

So we write the total solution as

y(n)=yh(n)+yp(n)

Note that if we are given a nonhomogeneous difference equation with initial conditions, we first find yh(n) and do not evaluate the constants associated with yh(n) because these initial conditions are given for the total solution y(n). The following example will illustrate this point.

Example 2.19

Consider the system described by the difference ...

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