Time Domain Analysis of Discrete-Time Systems
This module covers the analysis of Discrete-Time Linear Time-Invariant (DT-LTI) systems, focusing on their behavior in the time domain. Understanding these systems is essential for various engineering fields such as digital signal processing and control systems. The module introduces core concepts such as impulse response, convolution, and the representation of DT-LTI systems via difference equations and block diagrams.
Sections
Navigate through the learning materials and practice exercises.
What we have learnt
- The impulse response uniquely characterizes a DT-LTI system.
- Convolution is the primary mathematical operation that links input signals and output responses in DT-LTI systems.
- Causality and stability are critical properties for the functionality of discrete-time systems.
Key Concepts
- -- Impulse Response
- The response of a DT-LTI system to an impulse input, which uniquely characterizes the system's behavior.
- -- Convolution
- A mathematical operation that combines two sequences to produce a third, representing the output of an LTI system based on its impulse response and input signal.
- -- Causality
- A property of a DT-LTI system whereby the output at any time depends only on current and past input values.
- -- Stability (BIBO)
- A property ensuring that every bounded input results in a bounded output; guarantees predictable system behavior.
- -- Difference Equation
- An equation that relates the current output of a system to its current and past input and output values, used to model DT-LTI systems.
Additional Learning Materials
Supplementary resources to enhance your learning experience.