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EE 314 Signal and Linear System Analysis

EE 314 Signal and Linear System Analysis. Linear Time-Invariant Systems. Summary of Last Lecture. Total Energy Average Power. Sum of power Time. Energy / Time. Linear Time-Invariant Systems. A system produces an output signal in response to stimulus from an input signal.

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EE 314 Signal and Linear System Analysis

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  1. EE 314 Signal and Linear System Analysis Linear Time-Invariant Systems EE 314 Signal and Linear System Analysis

  2. Summary of Last Lecture • Total Energy • Average Power Sum of power Time Energy / Time EE 314 Signal and Linear System Analysis

  3. Linear Time-Invariant Systems • A system produces an output signal in response to stimulus from an input signal. • What is a Linear Time-Invariant (LTI) System? • A Linear system produces an output that is a linear function of the input • A Time-Invariant system produces an output that is NOT explicitly dependent on time • A time-shifted input results in an only time-shifted output!! Input Output EE 314 Signal and Linear System Analysis

  4. Linear Time-Invariant SystemsLinear Systems • A function f(…) is said to be linear if: • Scaling Property: • Additivity Property: • Is the function a linear function? • Assume, m and c to be constants. EE 314 Signal and Linear System Analysis

  5. Linear Time-Invariant SystemsLinear Systems • Scaling Property: • Consider the following: If I double the input will the output double? EE 314 Signal and Linear System Analysis

  6. Linear Time-Invariant SystemsLinear Systems • It the system scalable? • Given the relationship between the input () and output (): • Is the system scalable? If I double the input will the output double? If, x = c x and y = c y, Is the eqn unchanged? Input Output System EE 314 Signal and Linear System Analysis

  7. Linear Time-Invariant SystemsLinear Systems • Additivity Property: • Also known as the superposition property!! • An Example: Determine the current I in resistor R2 EE 314 Signal and Linear System Analysis

  8. Linear Time-Invariant SystemsLinear Systems • Time-Invariant Systems: • A system is time-invariant if a time shift in the input results only in the same time shift in the output EE 314 Signal and Linear System Analysis

  9. Linear Time-Invariant SystemsLinear Systems MATLAB Code Lecture_05_LTI_systems.m • Some Examples: Linear? System Time Invariant? Scaling? Additive? Yes Yes Yes Yes Yes No No No Yes Yes Yes No No No Yes EE 314 Signal and Linear System Analysis

  10. Linear Time-Invariant SystemsLinear Systems • Graphical review of System System y Is this a TI system? y EE 314 Signal and Linear System Analysis

  11. Next Lecture • Impulse Response of LTI Systems • Reading Assignment: Chap. 2.2 EE 314 Signal and Linear System Analysis

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