EGEE 4110 Digital Signal Processing Lecture 3

1
EGEE 4110Digital Signal ProcessingLecture 3

• Systems Review
• Professor Timothy Tuinstra

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Linear Shift Invariant (LSI) Systems

• Characterizing LSI systems

Difference Equation Impulse Response Transfer
Function State Space
xn
yn
Discrete System
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Discrete Convolution

• Convolution is how we relate the input xn of a
  system to the output yn of the system given we
  know its impulse response hn.
• Discrete convolution is defined by

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System Stability

• A discrete filter is said to be Bounded Input
  Bounded Output (BIBO) stable if for any bounded
  input, the output of the filter is also bounded.
• The critical question for the engineer is,
• How do I know if my system is BIBO stable?

5
DSP Stability Theorem

• An LSI system is BIBO stable iff its impulse
  response is absolutely summable, that is,

• Implication FIR filters are always stable!