**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

- Appendix D (Laplace Transform Analysis)
- Assignment 2
**Lecture Videos (Total Viewing Time 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]

- Transfer Functions, Partial Fraction Expansion, Repeated Poles
[44:52]

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