EEE 301: Continuous Signals and Linear Systems
January 2017 Semester
Level-3 Term-I
Section-C
Class: 3 hours/week
Course content:
Classification of signals and systems: signals- classification, basic operation on signals, elementary signals, representation of signals using impulse function; systems- classification. Properties of Linear Time Invariant (LTI) systems: Linearity, causality, time-invariance, memory, stability, invertibility.
Time domain analysis of LTI systems: Differential equations- system representation, order of the system, solution techniques, zero state and zero input response, system properties; impulse response- convolution integral, determination of system properties; state variable- basic concept, state equation and time domain solution.
Frequency domain analysis of LTI systems: Fourier series- properties, harmonic representation, system response, frequency response of LTI systems; Fourier transformation properties, system transfer function, system response and distortion less systems. Applications of time and frequency domain analyses: solution of analog electrical and mechanical systems, amplitude modulation and demodulation, time-division and frequency-division multiplexing.
Laplace transformation: properties, inverse transform, solution of system equations, system transfer function, system stability and frequency response and application.
Class Tests and Assignments:
Class Test 1 Syllabus
- Continuous-Time vs Discrete-Time Signals
- Periodic vs Aperiodic Signals
- Energy and Power Signals
- Transformation of the Independent Variable
- The Shifting Operation
- The Reflection Operation
- The Time-Scaling Operation
- Even and Odd Signals
- Elementary Signals
- Unit Step Function
- Ramp Function
- Signum Function
- Unit Impulse Function
- Properties of Unit Impulse Function
- Derivatives of Unit Impulse Function
- Properties of Derivatives of Unit Impulse Function
Date: 22 March, 2017 (Wednesday)
Time: 9:00 am
Venue: ECE 539
Instructions:
1. Closed book exam.
2. Exam duration: 40 min.
3. Total no. of questions: 7.
4. Bring a stapler with you to staple extra pages.
5. Any kind of cheating will be heavily penalized.
Class Test 2 Syllabus
- Classification of Continuous Time Systems
- Linear and Nonlinear Systems
- Time Varying and Time-Invariant Systems
- Systems with Memory and without Memory
- Causal Systems
- Invertibility and Inverse Systems
- Stable Systems
- Linear Time-Invariant Systems
- The Convolutional Integral
- Graphical Interpretation of Convolution
- Properties of Linear, Time-Invariant Systems
- Memoryless LTI Systems
- Causal LTI Systems
- Invertible LTI Systems
- Stable LTI Systems
- Systems Described by Differential Equation
- Linear Constant Co-efficient Differential Equations
- Basic System Components
- Block Diagram
- Zero-input and Zero-state Output
- Finding Impulse Response
- State-Variable Representation
- State Equations
- Time-Domain Solution of the State Equations
- Canonical Forms
- Stability Considerations
Date: 24 April, 2017 (Monday)
Time: 8:30 am
Venue: ECE 539
Want to know more on finding impulse response, click here.
Class Test 3 Syllabus
- Orthogonal Representations of Signals
- The Exponential Fourier Series
- Trigonometric Fourier Series
- Dirichlet Conditions
- Properties of Fourier Series
- Effects of Symmetry
- Linearity
- Products of Two Signals
- Convolution of Two Signals
- Parseval's Theorem
- Shift in Time
- Differentiation and Integration of Periodic Signals
- Systems with Periodic Input
- Gibbs Phenomenon
Date: 8 May, 2017 (Monday) 6 May, 2017 (Saturday)
Time: 8:30 am
Venue: ECE 539