Signals and Systems

Syllabus

←Previous Lesson: IntroductionNext Lesson: Sinewaves →


Part 1: Sinewaves and Linear Time-Invariant Systems

  1. Playing with Sinewaves
  2. Shifting and Scaling
  3. The Linear Pendulum system
  4. Linearity
  5. Time-Invariance
  6. Other fun signals: Square Waves, Triangle Waves, Unit Steps
  7. The Complex Exponential
  8. RC Circuits (or why we love complex numbers)
  9. The complex exponential as an Eigenfunction

Part 2: Fourier Series Representation

  1. The Inner Product (or how many peas are in my soup?)
  2. Orthogonal Functions
  3. Decomposing Periodic Signals
  4. Signal Energy and Average Power
  5. The (Sine) Fourier Series
  6. Even and Odd Signals
  7. The Cosine Fourier Series
  8. Dealing with Offsets
  9. The Sine/Cosine Fourier Series
  10. The Complex Fourier Series
  11. Fourier Series with Time Instead of x
  12. Plotting the Fourier Series
  13. Changing the Period - What happens to the Frequencies?
  14. Parseval's Theorem
  15. A real-world example: Transfer Functions - RC circuits and square waves

Part 3: The Fourier Transform and its Applications

  1. Stretching the Period
  2. The limit as the period becomes infinite
  3. Examples of the Fourier Transform
  4. Filtering
  5. The Transfer function
  6. The RC circuit and its cousins: First-order systems
  7. The RLC circuit and its cousins: Second-order systems
  8. Modulation and frequency-shifting

Part 4: Time-Domain Analysis of Systems

  1. The Impulse 'Function'
  2. The Impulse Response
  3. The transfer function and the impulse response
  4. Response to A bunch of impulses: Convolution
  5. Response to a continuous function
  6. The convolution integral
  7. The convolution integral and the Fourier Transform

Part 5: The Laplace Transform

  1. When does the Fourier Transform not exist? Stability
  2. The Laplace Transform
  3. The Laplace Transform graphically
  4. When to use the Laplace Transform
  5. Region of Convergence
  6. The inverse Laplace Transform

Additional Things to cover I haven't added yet

  • Causality
  • Stability
  • Fourier Series Convergence
  • Parseval's Theorem
  • Properties of the Fourier series (teach by example)
  • Properties of the Fourier Transform
  • Replacing the derivative with \(j\omega\)
  • Unilateral vs. bilateral Laplace transform
Some stuff

Planned For

  1. Power
  2. Inner products

    3. A quiz question


    ←Previous Lesson: IntroductionNext Lesson: Sinewaves →


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