Consider an LTI system described by the following block diagram The overall

# Consider an lti system described by the following

• 48

This preview shows page 39 - 48 out of 48 pages.

Consider an LTI system described by the following block diagram The overall system function can be computed as 4-May-19 EIE3001 Sig & Sys, Spring 2019 39 * We have used the convolution property and linearity property to arrive at the result.

Subscribe to view the full document.

Example 1: First-order System with a Feedback Loop Consider a causal LTI system with the following system function Method 1: Use the formula from the previous slide, which yields H 1 ( z ) = 1, 4-May-19 EIE3001 Sig & Sys, Spring 2019 40
Example 1: First-order System with a Feedback Loop Consider a causal LTI system with the following system function Method 2: First compute the difference equation in time domain Then the diagram follows 4-May-19 EIE3001 Sig & Sys, Spring 2019 41

Subscribe to view the full document.

Example 2: System with Both Forward and Feedback Consider a causal LTI system with the following system function This system can be considered as the cascade of two systems: 4-May-19 EIE3001 Sig & Sys, Spring 2019 42
Example 2: System with Both Forward and Feedback Consider a causal LTI system with the following system function This system can be considered as the cascade of two systems: 4-May-19 EIE3001 Sig & Sys, Spring 2019 43

Subscribe to view the full document.

Example 3: Second-order System Consider a causal LTI system with the following system function Method 1: Direction inspection. First obtain the difference equation and then rearrange the terms: 4-May-19 EIE3001 Sig & Sys, Spring 2019 44
Example 3: Second-order System Consider a causal LTI system with the following system function Method 2: Cascade method. From the system can be considered as the cascade of two first-order feedback systems: 4-May-19 EIE3001 Sig & Sys, Spring 2019 45

Subscribe to view the full document.

Example 3: Second-order System Consider a causal LTI system with the following system function Method 2: Cascade method. From the system can be considered as the cascade of two first-order feedback systems: 4-May-19 EIE3001 Sig & Sys, Spring 2019 46
Example 3: Second-order System Consider a causal LTI system with the following system function Method 3: Parallel-form. Apply partial series expansion the system can be considered as the linear combination of two first-order feedback systems: 4-May-19 EIE3001 Sig & Sys, Spring 2019 47

Subscribe to view the full document.

Summary ¾ Expected learning outcome Understand the relationship between z-transform and DTFT Be able to represent discrete-time signals using z-transform Be able to apply the properties of z-transform Be able to compute inverse z-transform using inspection and partial-series expansion techniques Be able analyze LTI systems using z-transform ¾ Suggested reading: Sections 10.1—10.3, 10.5—10.8. 4-May-19 EIE3001 Sig & Sys, Spring 2019 48
• Fall '13

### What students are saying

• As a current student on this bumpy collegiate pathway, I stumbled upon Course Hero, where I can find study resources for nearly all my courses, get online help from tutors 24/7, and even share my old projects, papers, and lecture notes with other students.

Kiran Temple University Fox School of Business ‘17, Course Hero Intern

• I cannot even describe how much Course Hero helped me this summer. It’s truly become something I can always rely on and help me. In the end, I was not only able to survive summer classes, but I was able to thrive thanks to Course Hero.

Dana University of Pennsylvania ‘17, Course Hero Intern

• The ability to access any university’s resources through Course Hero proved invaluable in my case. I was behind on Tulane coursework and actually used UCLA’s materials to help me move forward and get everything together on time.

Jill Tulane University ‘16, Course Hero Intern