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Introduction to Linear, Time-Invariant Systems

February 8, 2019 by 3200 Creative

Linear, time-invariant (LTI) systems are the primary signal-processing tool for modeling the action of a physical phenomenon on a signal, such as propagation and measurement. LTI systems also are a very important tool for processing signals. For example, filters are almost always LTI systems. In this lesson you will learn the definition of a system and the important system properties of linearity, time-invariance, and causality.

There are four different common methods for relating the input of an LTI system to the output. You will also gain an introductory understanding of these methods for describing the action of systems. Different methods for describing the system behavior are used because they reveal different system attributes. Future lessons will study these four descriptions in more depth.

Prerequisites

  • Complex Sinusoids
  • Exponential, Step, and Impulse Signals

Key Concepts and Screenshots

Concepts and Screenshots for Introduction to Linear, Time-Invariant Systems

QuizzesStatus
1

Introduction to Linear Time Invariant Systems

2

Intro to Linear Time-Invariant Systems Exercises


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Course Lessons

  • Signals Everywhere

  • Ever-Present Noise

  • Models, Math, and Real-World Signals

  • Four Signal-Processing Themes

  • Jupyter Notebook: Explore FIR Filtering

  • Jupyter Notebook: Explore Image Filtering

  • Building Signals with Blocks: Basis Expansions

  • Signals: The Basics

  • Sinusoidal Signals

  • Sinusoidal Signals Examples

  • Complex Sinusoids

  • Exponential, Step, and Impulse Signals

  • Introduction to Linear, Time-Invariant Systems

  • Introduction to Difference Equation System Descriptions

  • Impulse Response Descriptions for LTI Systems

  • Frequency Response Descriptions for LTI Systems

  • Introduction to the System Function and System Poles and Zeros

  • The Four Fourier Representations

  • Summary Problems for Foundations

Courses

  • Foundations

  • Time Domain LTI Systems

  • Fourier Series and Transforms

  • Sampling and Reconstruction

  • The DFT and Applications

  • The Z-Transform

  • Intro to Filter Design

  • IIR Filter Design

  • FIR Filter Design

  • Random Signal Characterization

  • Basis Representations of Signals

  • Estimation of Power Spectra and Coherence

  • Introduction to Signal Estimation and Detection Theory

  • MMSE Filtering and Least-Squares Problems

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