2011 | OriginalPaper | Chapter

# Difference equations and the Z transform

Convert the descriptive prescription of the output form of a sequence into a recursive description and recognise the importance of initial terms Recognise a difference equation, determine its order and generate its terms from a recursive description Obtain the solution to a difference equation as a sum of the homogeneous solution and the particular solution Define the Z transform of a sequence and derive transforms of specified sequences Make reference to a table of standard Z transforms Recognise the Z transform as being a linear transform and so obtain the transform of linear combinations of standard sequences Apply the first and second shift theorems, the translation theorem, the initial and final value theorems and the derivative theorem Use partial fractions to derive the inverse transforms Use the Z transform to solve linear, constant coefficient difference equations Create a sequence by sampling a continuous function and demonstrate the relationship between the Laplace and the Z transform