EE203-SUNYBuffalo-16-Chapter12-02

EE203-SUNYBuffalo-16-Chapter12-02 - SMALL for Big Things...

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Unformatted text preview: SMALL for Big Things University at Buffalo SMALL for Big Things University at Buffalo nanobioSensors & MicroActuators Learning Lab The State University of New York nanobioSensors & MicroActuators Learning Lab The State University of New York Functional Transforms EE 203 Circuit Analysis 2 Lecture 16 Chapter 12.4 Functional Transforms Kwang W. Oh, Ph.D., Assistant Professor SMALL (nanobioSensors and MicroActuators Learning Lab) Department of Electrical Engineering University at Buffalo, The State University of New York 215E Bonner Hall, SUNY-Buffalo, Buffalo, NY 14260-1920 Tel: (716) 645-3115 Ext. 1149, Fax: (716) 645-3656 E-mail: kwangoh@buffalo.edu, http://www.SMALL.Buffalo.edu EE 203 Circuit Analysis 2 | Spring 2008 | Prof. Kwang W. Oh | EE@SUNY-Buffalo Lecture 16 | Chapter 12 | 2/5 | 1/14 EE 203 Circuit Analysis 2 | Spring 2008 | Prof. Kwang W. Oh | EE@SUNY-Buffalo Lecture 16 | Chapter 12 | 2/5 | 2/14 SMALL for Big Things University at Buffalo SMALL for Big Things University at Buffalo nanobioSensors & MicroActuators Learning Lab The State University of New York nanobioSensors & MicroActuators Learning Lab The State University of New York Step Function: u(t), Decaying Exponential Function: e-at Sinusoidal Function: sin ωt Unit Step Function: u(t) Decaying Exponential Function: e-at The integration across the discontinuity discontinuity at the origin is zero. EE 203 Circuit Analysis 2 | Spring 2008 | Prof. Kwang W. Oh | EE@SUNY-Buffalo Lecture 16 | Chapter 12 | 2/5 | 3/14 EE 203 Circuit Analysis 2 | Spring 2008 | Prof. Kwang W. Oh | EE@SUNY-Buffalo Lecture 16 | Chapter 12 | 2/5 | 4/14 SMALL for Big Things University at Buffalo SMALL for Big Things University at Buffalo nanobioSensors & MicroActuators Learning Lab The State University of New York nanobioSensors & MicroActuators Learning Lab The State University of New York EE 203 Circuit Analysis 2 Lecture 16 Chapter 12.5 Operational Transforms Kwang W. Oh, Ph.D., Assistant Professor SMALL (nanobioSensors and MicroActuators Learning Lab) Department of Electrical Engineering University at Buffalo, The State University of New York 215E Bonner Hall, SUNY-Buffalo, Buffalo, NY 14260-1920 Tel: (716) 645-3115 Ext. 1149, Fax: (716) 645-3656 E-mail: kwangoh@buffalo.edu, http://www.SMALL.Buffalo.edu EE 203 Circuit Analysis 2 | Spring 2008 | Prof. Kwang W. Oh | EE@SUNY-Buffalo Lecture 16 | Chapter 12 | 2/5 | 5/14 EE 203 Circuit Analysis 2 | Spring 2008 | Prof. Kwang W. Oh | EE@SUNY-Buffalo Lecture 16 | Chapter 12 | 2/5 | 6/14 SMALL for Big Things University at Buffalo SMALL for Big Things University at Buffalo nanobioSensors & MicroActuators Learning Lab The State University of New York nanobioSensors & MicroActuators Learning Lab The State University of New York Operational Transforms Multiplication, Addition / Substration Multiplication by a constant Addition / Subtraction Differentiation Integration Translation in the time domain Translation in the frquency domain Scale changing EE 203 Circuit Analysis 2 | Spring 2008 | Prof. Kwang W. Oh | EE@SUNY-Buffalo Multiplication by a Constant Addition / Subtraction Lecture 16 | Chapter 12 | 2/5 | 7/14 EE 203 Circuit Analysis 2 | Spring 2008 | Prof. Kwang W. Oh | EE@SUNY-Buffalo Lecture 16 | Chapter 12 | 2/5 | 8/14 SMALL for Big Things University at Buffalo SMALL for Big Things University at Buffalo nanobioSensors & MicroActuators Learning Lab The State University of New York nanobioSensors & MicroActuators Learning Lab The State University of New York Differentiation Integration-By-Parts ∞ = ∫ − udv 0 ∞ u = e − st , dv = ∞ = uv 0− − ∫ − vdu 0 [ ]dt, df ( t ) dt v = f (t ) d (uv) = udv + vdu ∫ d (uv) = uv = ∫ udv + ∫ vdu ∴ ∫ udv = uv − ∫ vdu EE 203 Circuit Analysis 2 | Spring 2008 | Prof. Kwang W. Oh | EE@SUNY-Buffalo Lecture 16 | Chapter 12 | 2/5 | 9/14 EE 203 Circuit Analysis 2 | Spring 2008 | Prof. Kwang W. Oh | EE@SUNY-Buffalo Lecture 16 | Chapter 12 | 2/5 | 10/14 SMALL for Big Things University at Buffalo SMALL for Big Things University at Buffalo nanobioSensors & MicroActuators Learning Lab The State University of New York nanobioSensors & MicroActuators Learning Lab The State University of New York Integration Translation in the Time Domain Translation Translation in the time domain corresponds to multiplication by an exponential in the frequency domain. Example ∞ = ∫ − udv 0 ∞ ∞ = uv 0− − ∫ − vdu 0 EE 203 Circuit Analysis 2 | Spring 2008 | Prof. Kwang W. Oh | EE@SUNY-Buffalo Lecture 16 | Chapter 12 | 2/5 | 11/14 EE 203 Circuit Analysis 2 | Spring 2008 | Prof. Kwang W. Oh | EE@SUNY-Buffalo Lecture 16 | Chapter 12 | 2/5 | 12/14 SMALL for Big Things University at Buffalo SMALL for Big Things University at Buffalo nanobioSensors & MicroActuators Learning Lab The State University of New York nanobioSensors & MicroActuators Learning Lab The State University of New York Translation in the Frequency Domain Scale Changing Translation Translation in the frequency domain corresponds to multiplication by an exponential in the time domain. The The scale-change property gives the relationship between f(t) and F(s) when the time variable is multiplied by a positive constant: Example Example EE 203 Circuit Analysis 2 | Spring 2008 | Prof. Kwang W. Oh | EE@SUNY-Buffalo Lecture 16 | Chapter 12 | 2/5 | 13/14 EE 203 Circuit Analysis 2 | Spring 2008 | Prof. Kwang W. Oh | EE@SUNY-Buffalo Lecture 16 | Chapter 12 | 2/5 | 14/14 ...
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This note was uploaded on 10/19/2011 for the course EE 203 taught by Professor Staff during the Spring '08 term at SUNY Buffalo.

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