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Understanding Convolution and Integral in Linear Time-Invariant Systems

This lecture delves into the essential concepts of convolution and integral in linear time-invariant (LTI) systems. It covers the impulse response, transfer function of LTI systems, and key properties such as linearity and time invariance. We discuss the importance of convolution in determining system outputs for given inputs, particularly focusing on zero-state responses and graphical convolution techniques. Through examples, including infinite duration inputs and impulse responses, students will gain a solid understanding of these fundamental principles in signals and systems.

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Understanding Convolution and Integral in Linear Time-Invariant Systems

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  1. Lecture #03 Convolution sum & Integral

  2. Linear system Convolution Integral : LTI system LTI system … signals & systems

  3. Linear system LTI system I.C.=0 Impulse response Transfer function of the system LTI system I.C.=0 Any input Zero state response signals & systems

  4. Linear system Example : Graphical convolution (1) signals & systems

  5. Linear system (2) (3) signals & systems

  6. Linear system (4) (5) signals & systems

  7. Linear system Ans: signals & systems

  8. Convolution sum signals & systems

  9. LTI system Only true for linear system (linearity property) x[k] is a constant with respect to H (linearity property) Let Only true for time invariant system Convolution sum signals & systems

  10. convolution signals & systems

  11. signals & systems

  12. Example 2.1 Impulse response signals & systems

  13. Example 2.2 The input and impulse response are of infinite duration Consider a system with impulse response Find y[n] when the input is x[n]=u[n] signals & systems

  14. signals & systems

  15. signals & systems

  16. signals & systems

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