A Simple and Elegant Method for Computing the Inverse Z-transform of Rational Functions

Finding the inverse z-transform of a rational function is usually considered a completely routine task with nothing special to say about it. However, practically all the procedures described in the engineering literature for doing this task can be very laborious for manual calculation when the function whose inverse z-transform is sought has multiple poles. This is often a problem for students when solving homework and exam tasks. The situation is particularly awkward when the poles are ugly numbers. Additionally, the described procedures are very unsuitable for programming on a computer. This paper proposes a simple, elegant and student-friendly way to calculate the inverse z-transform of a rational function. In addition to the basic variant, which is most suitable for manual calculation when the poles are relatively nice numbers, there are also variants that may be more suitable in other cases, including a variant that is extremely suitable for programming on a computer, even on the programmable calculators.