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Convolution Integral

Convolution Integral. Prof. Siripong Potisuk. CT Unit Impulse. Continuous-time impulse function Properties:. Representation of CT Signals Using Unit Impulses. (Impulse Decomposition). Approximate x ( t ) as a sum of time-shifted and scaled pulses. Impulse Response.

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Convolution Integral

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  1. Convolution Integral Prof. Siripong Potisuk

  2. CT Unit Impulse • Continuous-time impulse function • Properties:

  3. Representation of CT Signals Using Unit Impulses (Impulse Decomposition) Approximate x(t) as a sum of time-shifted and scaled pulses

  4. Impulse Response Convolution Integral Response of a CT LTI System

  5. Graphical Method for Computing Convolution Integral

  6. Properties of Convolution Integral 1) Commutative Property 2) Distributive Property

  7. 3) Associative Property

  8. 4) Causality - The impulse response of a causal LTI system must be zero before the impulse occurs. - Causality for a linear system is equivalent to the condition of initial rest. 5) BIBO stability A necessary and sufficient condition fora CT LTI system to be BIBO stable is that the impulse response is absolutely integrable.

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