Convolution Integral

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Convolution Integral

• Prof. Siripong Potisuk

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CT Unit Impulse

• Continuous-time impulse function
• Properties

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Representation of CT Signals Using Unit Impulses
(Impulse Decomposition)
Approximate x(t) as a sum of time-shifted
and scaled pulses
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Response of a CT LTI System
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Graphical Method for Computing Convolution
Integral
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Properties of Convolution Integral
1) Commutative Property
2) Distributive Property
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3) Associative Property
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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 for a CT LTI
system to be BIBO stable is that the impulse
response is absolutely integrable.