1. Research Institute for Future Media Computing
未来媒体技术与计算研究所
Research Institute for Future Media Computing
Tutorial
4. Fourier Transform & Z Transform
江健民，国家千人计划特聘教授
深圳大学未来媒体技术与计算研究所所长
Office Room: 409

2. Additional Points about Fourier and z transforms
For discrete signals, x(nT) is often regarded or rewritten as x(n), to emphasize the discrete signal strength at the instant n;
In practice, FFT plays important role for a range of applications relevant to signal processing, and you only need to know how to use the existing software module;
z-transform is a powerful tool for discrete signal sequence analysis and discrete systems, especially for all digital filters, including FIRs and IIRs etc.
For standard z-transform representation, there exists a regular long-division formulation to obtain its inverse transform as given below:

3. Exercise-4.1 Use the above formulation to verify the inverse z-transform for the example as given in the lecture.

4. Properties of the z-transform
Linearity:
Delays or shifts:
Convolution:
System descriptions:

5. Numerator example: Denominator example: + + X(z) Y(z) Z-1 X(z) Y(z)