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Graphical Convolution Analysis for Causal LTI Systems

Summary of applying causal input to causal LTI systems graphically, evaluating convolution, and MATLAB code for series and parallel systems. Exploring causality in LTI systems and examples. Next lecture preview on LTI sinusoidal response.

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Graphical Convolution Analysis for Causal LTI Systems

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  1. EE 314 Signal and Linear System Analysis Graphical Convolution EE 314 Signal and Linear System Analysis

  2. Summary of Last Lecture • Applying a causal input () to a causal LTI systems with impulse response gives rise to a causal output EE 314 Signal and Linear System Analysis

  3. Graphical Convolution • Revisiting the prior RC example • Let , hence, • Input: • Analytical soln is: • For, 0 < t < 1 EE 314 Signal and Linear System Analysis

  4. Graphical Convolution • For, t > 1 • Final result EE 314 Signal and Linear System Analysis

  5. Graphical Convolution EE 314 Signal and Linear System Analysis

  6. Graphical Convolution • Let’s evaluate the convolution graphically • Overlay a plot of with a plot of , compute the area under the product (for ), then vary . The area under the product!! We need => Shift then flip => Flip then shift Shift by then flip We need OR= Flip then shift by EE 314 Signal and Linear System Analysis

  7. Graphical Convolution • Start with The area under the product? EE 314 Signal and Linear System Analysis

  8. Graphical Convolution • Now, consider EE 314 Signal and Linear System Analysis

  9. Graphical Convolution • Now, consider EE 314 Signal and Linear System Analysis

  10. Graphical Convolution MATLAB code EE 314 Signal and Linear System Analysis

  11. Graphical Convolution • Systems connected in series • Systems connected in parallel EE 314 Signal and Linear System Analysis

  12. Causal LTI System • Causality • A LTI system is causal if it does NOT rely on future inputs in order to determine the current output. • All real/physical systems are causal – They can not anticipate future inputs!! • i.e., A causal system has an impulse response that is a causal function. Does this system have memory? Consider Give an example of a system that does NOT have memory? Would use future values of to determine !! EE 314 Signal and Linear System Analysis

  13. Next Lecture • LTI Sinusoidal Response • Reading Assignment: Chap. 2.7 EE 314 Signal and Linear System Analysis

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