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Lab02s09 - 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 #2: Introduction to Complex Exponentials Date: 20–26 Jan. 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 . One of the laboratory instructors must verify the appropriate steps by signing on the Instructor Verification line. When you have completed a step that requires verification, simply raise your hand and demonstrate the step to the TA or instructor. After completing the warm-up section, turn in the verification sheet to your TA before leaving the lab. It is only necessary to turn in Section 4 as the lab report for this lab. More information on the lab report format can be found on t-square under the INFO link. Please label the axes of your plots and include a title for every plot. In order to reduce “orphan” plots, include each plot as a figure embedded within your report. For more information on how to include figures and plots from M ATLAB in your report file, consult the INFO link on t-square , or ask your TA for details. 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. Due Date: The lab report will be due during the period 27-Jan.–2-Feb. at the start of your lab. PRINTING BUDGET: For the printers in the ECE labs, you have a quota. Please limit your printing to es- sential items for the labs. If you need to print lecture slides and other large documents, use the central (OIT) printing facilities. 1 Introduction and Overview The goal of this laboratory is to gain familiarity with complex numbers and their use in representing sinu- soidal signals such as x.t/ D A cos .!t C '/ as complex exponentials z.t/ D Ae j' e j!t . The key is to use the complex amplitude, X D Ae j' , and then the real part operator applied to Euler’s formula: x.t/ D < e f Xe j!t g D < e f Ae j' e j!t g D A cos .!t C '/ Manipulating sinusoidal functions using complex exponentials turns trigonometric problems into simple arithmetic and algebra. In this lab, we first review the complex exponential signal and the phasor addition property needed for adding cosine waves. Then we will use M ATLAB to make plots of phasor diagrams that show the vector addition needed when combining sinusoids.
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