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Models, Math, and Real-World Signals

February 8, 2019 by 3200 Creative

In this third lesson on fundamental signal processing concepts you will learn about the role of mathematical models in signal processing. Models are used to describe characteristics of signals and or noise that are relevant to the information of interest in the signal. Mathematical models underlie all algorithms in signal processing, including separation of signals and noise, signal compression, and estimation of signal parameters.

Systematic approaches to signal processing algorithm design and performance analysis are possible because of the reliance on mathematical models. Understanding this concept will further develop your foundation and set the context for your further studies of signal-processing algorithms.

Key Concepts and Transcript

Concepts and Transcript for Models, Math, and Real-World Signals

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Math Models and Real World Signals


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  • Signals Everywhere

  • Ever-Present Noise

  • Models, Math, and Real-World Signals

  • Four Signal-Processing Themes

  • Building Signals with Blocks: Basis Expansions

  • Jupyter Notebook: Explore FIR Filtering

  • Jupyter Notebook: Explore Image Filtering

  • 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

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  • 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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