LINEAR SYSTEMS2- SET3-VIDEO ACCESS
LINEAR SYSTEMS – SET3
INTRODUCTION
Linear Systems provides the foundational mathematical framework for analysing continuous-time and discrete-time signals and systems, which is critical for all subsequent studies in electrical, computer, and electronic engineering. The prerequisites required for this course include Calculus II, Differential Equations, Introductory Physics (Electricity & Magnetism), and an introductory programming course (e.g., in Python, MATLAB, or C). Familiarity with complex numbers is essential.
You will learn to model engineering systems, predict their behavior, and understand how they process information. The concepts learned in this course are directly applicable to areas such as circuit design, control systems, signal processing, communications, and filter design.
Key Learning Objectives:
· Represent and classify signals (continuous vs. discrete, periodic vs. aperiodic) and systems (linear, time-invariant, causal, stable).
· Model Linear Time-Invariant (LTI) systems using differential/difference equations and convolution.
· Apply the Fourier Series to analyze periodic signals and the frequency response of systems.
· Utilize the Fourier Transform to analyze aperiodic signals and understand frequency-domain concepts like filtering and modulation.
· Use Laplace Transform to analyze system stability, transient response, and transfer functions.
· Introduce the Z-Transform for the analysis of discrete-time systems and digital filters.
· Use computational tools (e.g., MATLAB or Python with SciPy) to simulate and analyze systems.
SET 3 TOPICS
1. Background
1.1 Complex Numbers
1.2 Sinusoids
1.3 Partial Fraction Expansion
2. Signals
2.1 Definition
2.2 Useful Signal Operations
2.3 Classification of Signals
2.4 Continuous-Time and Discrete-Time Signals
2.5 Analog and Digital signals
2.6 Periodic and aperiodic signals
2.7 Casual and non-casual
2.8 Some Useful signal models
2.9 Systems
3. Time-domain Analysis
3.1 The Zero-Input Response
3.2 The Unit impulse response 𝒉𝒕
3.3 Zero-state Response
3.4 Convolution
3.5 Convolution using graphical method
3.6 Classical solution of differential solutions
4. Fourier Series
4.1 Periodic signal representation by trigonometric Fourier series
4.2 Trigonometric Fourier Spectrum
4.3 The role of amplitude and phase spectra in Wave shaping
4.4 Exponential Fourier series
5. Fourier Transform
5.1 Transforms of some useful functions
5.2 Properties of the Fourier Transform
5.3 Signal transmission through LTIC
6. Laplace transform (Chapter 4)
6.1 Properties, definition and inverse of laplace transform
6.2 Relationship between Fourier and Laplace transforms
6.3 Determining and solving transfer functions
6.4 Step functions
6.5 Bode plots (poles and zeros included)
7. Filter design
7.1 Phase and group delay
7.2 Low pass, high pass, band stop and band pass filters
7.3 Design filters
8. Sampling and quantization
8.1 Sampling theorem and Nyquist criteria
8.2 Aliasing
8.3 Sample interpolation
8.4 Sample effects