Convolution Sum

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Convolution Sum

• Prof. Siripong Potisuk

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Response of a DT LTI System
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(Also referred to as Impulse response)
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Properties of Convolution Sum

• A discrete-time LTI system is completely
  characterized
• by its impulse response, i.e., completely
  determines its
• input-output behavior.
• ? There is only one LTI system with a given
  hn

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The Commutative Property
The role of h n and x n can be interchanged
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The Distributive Property
is equivalent to
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The Associative Property
is equivalent to
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Causality for LTI Systems
- 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.
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Stability for LTI Systems
A necessary and sufficient condition for an LTI
system to be BIBO stable is that the impulse
response is absolutely summable.