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EE 314 Signal and Linear System Analysis

Explore concepts like LTI, memory, block diagrams in discrete-time signal analysis. Understand difference equations, system properties, impulse responses, and causality in linear systems.

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EE 314 Signal and Linear System Analysis

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  1. EE 314 Signal and Linear System Analysis Discrete Time LTI Systems EE 314 Signal and Linear System Analysis

  2. Summary of Last Lecture • DT Signals • A discrete-time signal is periodic if • The DT version of a periodic continuous-time signal may NOT be periodic!!! • Even if is periodic it may have a different period than EE 314 Signal and Linear System Analysis

  3. Discrete Time LTI Systems • A Discrete-Time System • An example might be: • As a difference equation: • As a Block diagram (D is a 1-sample delay): Discrete LTI System Input Output Does this system have memory? EE 314 Signal and Linear System Analysis

  4. Discrete Time LTI Systems • A continuous differential eqn: • The discrete-time equivalent Does this system have memory? This is a difference equation!! EE 314 Signal and Linear System Analysis

  5. Discrete Time LTI Systems • More generally: • Autoregressive Moving Average (ARMA) Difference Eqn Continuous Time: Discrete Time: Differential Equation Difference Equation (left side of equation) (right side of equation) EE 314 Signal and Linear System Analysis

  6. Discrete Time LTI Systems • Linear Time-Invariance • Same for continuous as for discrete • A system is linear if it has the scaling and additivity properties. • A system is time-invariant if delaying the input only delays the output. • A system is LTI if it is both linear and time-invariant. • By inspection of the differential/difference eqn: • LTI systems have constant coefficients • ARMA difference equations with constant coefficients are Linear and Time Invariant (’s and ’s are constant) EE 314 Signal and Linear System Analysis

  7. Discrete Time LTI Systems • Consider Discrete-Time the system • Described by the difference equation • Develop a block diagram representation • Realize the LHS and then the RHS RHS   - + - + D D D D EE 314 Signal and Linear System Analysis

  8. Discrete Time LTI Systems • Properties of Discrete-Time Systems • Impulse response: • What is the impulse response of the MA system? Apply an impulse as the input!! n=0 n=1 n=2 EE 314 Signal and Linear System Analysis

  9. Discrete Time LTI Systems • General form of the impulse response • Continuous system • Discrete system EE 314 Signal and Linear System Analysis

  10. Discrete Time LTI Systems • System Causality • For a continuous-time LTI system • For a discrete-time LTI system EE 314 Signal and Linear System Analysis

  11. Discrete Time LTI Systems • Output of a Continuous vs Discrete System Continuous Time: Discrete Time: Discrete LTI System Continuous LTI System Input Input Output Output Return of the convolution!! EE 314 Signal and Linear System Analysis

  12. Next Lecture • Discrete Time Convolution • Reading Assignment: Chap. 7.5 EE 314 Signal and Linear System Analysis

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