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Lab12As09

# Lab12As09 - GEORGIA INSTITUTE OF TECHNOLOGY SCHOOL of...

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GEORGIA INSTITUTE OF TECHNOLOGY SCHOOL of ELECTRICAL and COMPUTER ENGINEERING ECE 2025 Spring 2009 Lab #12: (A) PeZ: Second-Order IIR Filters Date: 8–15 Apr. 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; it is a warm-up only. This part of Lab #12 will be worth 50 points; the second part of Lab #12 (next week) will also be 50 pts. 1 Introduction In this part of the lab, you will use PeZ to create filters with complex conjugate poles and zeros. These are called second-order filters because the denominator polynomial is a quadratic with two roots. Among the filters that can be created are all-pass filters and nulling filters, as well as bandpass filters. 2 PreLab 2.1 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 hOEnŁ in the n -domain, and the frequency response H.e j O ! / (the O ! -domain), the graphical user interface (GUI) called PeZ was written in M ATLAB 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 form or rational polynomial 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 0 b k z k 1 N X ` D 1 a ` z ` (1) To run PeZ , type pezdemo at the command prompt and you will see the GUI shown in Fig. 1. 2 1 The original PeZ was written by C. Ulmer; a later version by K. Kong is the one that we will use in this lab. Recent modifica- tions by Greg Krudysz have added new features such as movie-making capability. 2 The command pez will invoke the older version of PeZ which is distinguished by a black background in all the plot regions. 1

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Figure 1: GUI interface for pezdemo showing a second-order filter whose frequency response exhibits a notch for its stopband. Pole and zero locations are given in rectangular coordinates. The Gain , G in (1), was adjusted to G D 0:85 in order to make the frequency response equal to one in the passbands.
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