Section 2: Transfer-Function and Pole-Zero Analysis of Digital Filters, Analog and State Variable Filters, Digitizing Filters

• Reading:
  • Appendix D (Laplace Transform Analysis)

  • Chapter 6 (Z-transform),

  • Chapter 6 (Transfer Function Analysis)

  • Appendix E (Analog Filters)

  • Laplace Analysis of a Force-Driven Mass

  • Appendix I.3 (Bilinear Transform)

  • Supplementary: Digital State-Variable Filters

  • Supplementary: Interactive Möbius Transformation

• Assignment 2

• Lecture Videos (Total Viewing Time $\approx$ 3 Hours):
  • Transfer Functions, Partial Fraction Expansion, Repeated Poles [44:52]

  • Transfer Functions [50:43]

  • State Variable Analog Filters and Digitization [47:50]

  • Repeated Poles at s=0
    • One Pole at DC in the s Plane [14:17]
    • Mechanical Integrator using a Mass [3:46]
    • Integrator made by a Spring or Inductor [5:46]
    • One Pole at DC in the s Plane, Continued [1:31]
    • Frequency Response of an Integrator [5:05]
    • Repeated Poles at DC [4:16]
    • General Transfer Function of a Pile of Poles at DC [3:38]
    • Impulse Response of a Pile of Poles at DC [3:22]

  • Simplest Electrical LPF: RC lowpass; RLC Circuits: Resistor Equation V = IR, Capacitor Equation Q = CV, Inductor Equation V = L dI/dt; Kirchhoff Node and Loop Analysis: Kirchhoff Loop Constraint (Sum of voltages around a loop is zero), Kirchhoff Node Constraint (Sum of currents into a node is zero); Voltage Transfer Circuits, Laplace Transform Circuit Analysis, Transfer Function of RC LPF: Pole-Zero Analysis, Impulse Response, Time Constant of Decay, Bode Plot [21:39]

  • Bilinear Transform Frequency Mapping, Analog Computers, State Space Formulation, Physical Derivation of Bilinear Transform, State Variable [38:29]

  • Bilinear Transform = special case of Moebius Transformation [DON'T MISS THIS ONE!] [2:34]