Research Institute for Future Media Computing 未来媒体技术与计算研究所 Research Institute for Future Media Computing http://futuremedia.szu.edu.cn 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 Email: jianmin.jiang@szu.edu.cn http://futuremedia.szu.edu.cn

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:

Exercise-4.1 Use the above formulation to verify the inverse z-transform for the example 4.2.2 as given in the lecture.

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

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