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EE 314 Signal and Linear System Analysis

EE 314 Signal and Linear System Analysis. Graphical Convolution. Summary of Last Lecture. Applying a causal input ( ) to a causal LTI systems with impulse response gives rise to a causal output. Graphical Convolution. Revisiting the prior RC example Let , hence, I nput:

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EE 314 Signal and Linear System Analysis

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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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