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Unit 1 - Continuous-time and Discrete-time Signals and Systems
Topics include: Signal Energy and Power, Transformations of Independent Variable, Periodic Signals, Even and Odd Signals, Continuous-time Complex Exponential Signals, Continuous-time Harmonically Related Complex Exponential Signals, Periodicity of Continuous-time Complex Exponential Signals, Discrete-time Complex Exponential Signals, Discrete-time Harmonically Related Complex Exponential Signals, Periodicity of Discrete-time Complex Exponential Signals, Distinguishing Characteristics of Discrete-time Complex Exponential Signals, Continuous-time Unit Impulse and Unit Step Signals, Discrete-time Unit Impulse and Unit Step Signals, Basic System Properties, Systems With and Without Memory, Invertibility and Inverse System, Causality, Bounded-input/Bounded-output (BIBO) Stability, Time Invariance, Linearity.
01- Continuous-time and Discrete-time Signals and Systems: Lecture Notes
01- Continuous-time and Discrete-time Signals and Systems: Solutions Homework
Unit 2 - Continuous-time and Discrete-time LTI Systems
Topics include: Continuous-time Linear Time-Invariant (LTI) System, Impulse Response of Continuous-time LTI System, Formulation of Convolution Integral, Examples Using Convolution Integral to Find Zero-state Response of Continuous-time LTI System, Discrete-time LTI System, Impulse Response of Discrete-time LTI System, Formulation of Convolution Sum, Examples Using Convolution Sum to Find Zero-state Response of Discrete-time LTI System, Basic Properties of LTI Systems, LTI Systems With and Without Memory, Invertibility of LTI Systems, Causality of LTI Systems, Causality of Linear Systems, Condition of Initial Rest, Bounded-input / Bounded-output (BIBO) Stability of LTI Systems, Example Using Impulse Response to Ascertain Basic Properties of an LTI System, Unit Step Response of Continuous-time LTI System, Relationships Between Unit Step Response and Unit Impulse Response of Continuous-time LTI System, Unit Step Response of Discrete-time LTI System, Relationships Between Unit Step Response and Unit Impulse Response of Discrete-time LTI System.
02- Continuous-time and Discrete-time LTI Systems: Lecture Notes
02- Continuous-time and Discrete-time LTI Systems: Solutions Homework
Unit 3 - Constant-Coefficient Differential Equations
Topics include: Condition of Initial Rest, Incrementally Linear System, Systems Approach: Total Response = Zero-Input Response + Zero-State Response, Characteristic Roots = Characteristic Values = Eigenvalues = Natural Frequencies, Characteristic Modes = Natural Modes, Characteristic Roots Distinct, Real and Negative in Sign, Characteristic Roots Repeated, Real and Negative in Sign, Characteristic Roots Complex Conjugate Pair With Negative Real Parts, Finding Impulse Response Directly from Differential Equation, Zero-State Response by Convolution Integral, Classical Method: Total Response = Natural Response + Forced Response, Natural Response = Homogeneous Solution = Complementary Solution, Forced Response = Particular Solution, Asymptotic Stability of Causal LTI Systems, Comparison of Asymptotic Stability and Bounded-Input/Bounded-Output (BIBO) Stability.
03- Constant-Coefficient Differential Equations: Lecture Notes
03- Constant-Coefficient Differential Equations: Solutions Homework