• Skip to primary navigation
  • Skip to main content
  • Skip to primary sidebar

ALLSIGNALPROCESSING.COM

Learn signal processing online

  • Home
  • Courses
  • Courses
  • About
  • FAQ
  • My Account
  • Blog
  • News
  • Contact
  • Login
  • Logout
  • Get All Access

Introduction to the System Function and System Poles and Zeros

February 8, 2019 by 3200 Creative

This lesson will introduce you to another very useful description for LTI systems: the system function and poles and zeros. You will learn that the system function is a generalization of the frequency response description when the input is an exponentially damped complex sinusoid. Also, the system function for systems described by difference equations is a ratio of polynomials. The roots of the denominator and numerator polynomials are called the poles and zeros of the system.

The system function is a powerful tool for the signal-processing practitioner. It is used to study the conditions under which a system is causal, stable, and can be inverted. It is also used in design of filters. The pole and zero locations provide a lot of insight into system characteristics, such as frequency response.

Prerequisites

  • Frequency Response Descriptions for LTI Systems

Key Concepts and Screenshots

Introduction to the System Function and System Poles and Zeros

Supplementary Material

  • m-file: Introduction to the System Function and System Poles and Zeros
QuizzesStatus
1

Introduction to the System Function and System Poles and Zeros


← Previous Lesson Next Lesson →

Filed Under: Uncategorized

Primary Sidebar

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

Copyright © 2023 ALLSIGNALPROCESSING.COM | Site Design by 3200 Creative

  • Terms of Service
  • Privacy Policy
  • Contact