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Understanding Linear Systems: A Comprehensive Course Overview with Dr. Timothy R. Tuinstra

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Join Dr. Timothy R. Tuinstra as he explores the fundamentals of linear systems in this engaging course. From signal characterization to system functionality, you will learn how to analyze and design linear systems with desirable properties. The course covers essential topics including time domain description, Fourier analysis, impulse response, and state space representation. Develop a new perspective on signals and systems, understanding their inputs, outputs, and behaviors through mathematical foundations essential for electrical engineering and communication theory.

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Understanding Linear Systems: A Comprehensive Course Overview with Dr. Timothy R. Tuinstra

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  1. EGEE 3110 - Linear Systems 8.24.11 Dr. Timothy R. Tuinstra

  2. About Dr. T. • Growing Up • Bangor, MI

  3. About Dr. T. • Education: • BSEE, Cedarville University, 1996 • MSEE, University of Dayton, 1998 • Ph.D., University of Dayton, 2008

  4. About Dr. T. Dr. T. Kelly ? Iain Owen My Family:

  5. What in the world are we doing here? • We are here to study signals & systems and how they interact. • Signal – A set of information or data…a function…Any quantity that we can measure over time. • System – A set of interconnected entities that interact and produce some type of behavior. • Systems have inputs and outputs. • Inputs: What we do to the system • Outputs: How the system responds • Inputs and outputs are both signals

  6. The Big Picture A System Input (A Signal) What we do to the system Sometimes called excitation Output (A Signal) The System’s Behavior Note: A system can have more than one inputs or outputs.

  7. Example Systems

  8. Linear Systems Island Fourier Forrest Here Be Dragons! Differential Equation Domain LaPlacePenninsula Sea of NonLinear & Complex Systems

  9. What is a Linear System? Linear systems are systems which produce outputs that are proportional to their inputs. For example, if I double the input, I double the output. In addition, if x1 produces y1 and x2 produces y2, then in a linear system, x1 + x2 produces y1 + y2…this is called superposition.

  10. Key Questions for us in this course • How can we describe and characterize signals? • Given a linear system, H, • How do we describe its functionality? i.e. What does H do? • If I excite H by doing x to it, what does it do then? • Is H well-behaved? Or does it go unstable? • How can I design a linear system that has certain desireable properties? • This class gives you the tools to answer these questions.

  11. What we will be learning in this course... • Signal Description • Time Domain Description • Fourier Description • Learning the different ways to describe systems and how they relate is key in this course: • Differential/Difference Equations • Impulse Response • Frequency Response • Transfer Functions • State Space…if time permits

  12. This course provides a mathematical foundation for much of electrical engineering Signal Processing How do we build systems that modify signals in certain helpful ways? Communications Theory How do we transfer information from here to there or from now to later? Controls Theory How do we harness systems to make them do what we want them to do? Linear Systems Theory

  13. I want to give you a new worldview…a “Weltanschauung”…a way of seeing the world through the lens of linear systems

  14. Shall we begin?

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