Time Domain Analysis of Continuous-Time Systems
This module explores the analysis of continuous-time linear time-invariant (LTI) systems in the time domain, building from fundamental principles to advanced concepts like impulse and step responses, convolution integrals, and properties of LTI systems. Practical importance is placed on system behavior understanding through mathematical frameworks, as well as real-world applications such as feedback control systems and differential equations.
Sections
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What we have learnt
- Linear Time-Invariant systems are fundamental to signal processing and can be characterized by impulse and step responses.
- The convolution integral is key to determining the output of LTI systems based on input signals and impulse responses.
- Causality and stability are essential properties that define the realizability and predictability of LTI systems.
Key Concepts
- -- Linear TimeInvariant (LTI) Systems
- Systems that follow the principles of linearity and time-invariance, where the response to a linear combination of inputs is the same as the linear combination of the respective outputs.
- -- Impulse Response
- The output of an LTI system when presented with a Dirac delta function as input, serving as the system's unique fingerprint.
- -- Convolution Integral
- A mathematical operation that expresses the output of an LTI system as the integral of the product of the input signal and the system's impulse response, providing a method to analyze system responses.
- -- Causality
- A property of a system where the output at any given time depends only on past and present inputs, not future inputs.
- -- BIBO Stability
- A condition defining that every bounded input to a system results in a bounded output, crucial for system reliability.
Additional Learning Materials
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