z-transform of a sequence. We then obtain the z-transform of some important sequences and discuss useful properties of the transform.
Most of the results obtained are tabulated at the end of the Section.
The z-transform is the major mathematical tool for analysis in such areas as digital control and digital signal processing.
- understand sigma ( ) notation for summations
- be familiar with geometric series and the binomial theorem
- have studied basic complex number theory including complex exponentials
- define the z-transform of a sequence
- obtain the z-transform of simple sequences from the definition or from basic properties of the z-transform
2 Commonly used z-transforms
2.1 Unit impulse sequence (delta sequence)
2.2 Unit step sequence
2.3 The geometric sequence
3 Linearity property and applications
3.1 Linearity property
3.2 Trigonometric sequences
4 Further -transform properties
4.1 Multiplication of a sequence by
4.2 Multiplication of a sequence by
5 Shifting properties of the z-transform
5.1 Right shift theorems
5.2 Left shift theorems