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Unformatted text preview: GEORGIA INSTITUTE OF TECHNOLOGY SCHOOL of ELECTRICAL and COMPUTER ENGINEERING ECE 2025 Spring 2009 Lab #10: PeZ - The z , n , and O ! Domains Date: 2531 Mar. 2009 You should read the Pre-Lab section of the lab and do all the exercises in the Pre-Lab section before your assigned lab time. The Warm-up section of each lab must be completed during your assigned Lab time and the steps marked Instructor Verification must also be signed off during the lab time by one of the laboratory instructors. After completing the warm-up section, turn in the verification sheet to your TA. Forgeries and plagiarism are a violation of the honor code and will be referred to the Dean of Students for disciplinary action. You are allowed to discuss lab exercises with other students and you are allowed to consult old lab reports, but you cannot give or receive written material or electronic files. Your submitted work should be original and it should be your own work. NO lab report is required for this lab. Lab #10 will be worth 50 points. 1 PeZ: Introduction In order to build an intuitive understanding of the relationship between the location of poles and zeros in the z-domain, the impulse response hOEn in the n-domain, and the frequency response H.e j O ! / (the O !-domain), a graphical user interface (GUI) called PeZ was written in MATLAB for doing interactive explorations of the three domains. 1 PeZ is based on the system function, represented as a ratio of polynomials in z 1 , which can be expressed in either factored or expanded form as: H.z/ D B.z/ A.z/ D G M Y k D 1 .1 z k z 1 / N Y ` D 1 .1 p ` z 1 / D M X k D b k z k 1 N X ` D 1 a ` z ` (1) where M is the number of zeros and N the number of poles. The poles are f p ` g , and the zeros are f z k g . If the poles and zeros occur in pairs that satisfy the complex-conjugate property, then the following property holds: A polynomial with real coefficients has roots that are real, or occur in complex-conjugate pairs. The PeZ GUI is contained in the SP-First toolbox. To run PeZ , type pezdemo at the command prompt and you will see the GUI shown in Fig. 1. 1.1 Controls for PeZ using pezdemo The PeZ GUI is controlled by the Pole-Zero Plot where the user can add (or delete) poles and zeros, as well as move them around with the pointing device. For example, Fig. 1 shows a case where two (complex- conjugate) zeros have been added, and PeZ has automatically included two poles at z D so that the system is causal. The button named ZZ was used to add these zeros; the button PP would be used to add poles....
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