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Last updated:

September 19, 2022

Duration:

Unlimited Duration

FREE

This course includes:

Unlimited Duration

Badge on Completion

Certificate of completion

Unlimited Duration

Description

This course covers the fundamental methods used for exploring the information content of observations related to kinematical and dynamical models

Course Curriculum

  • Table of Contents Unlimited
  • Preface Unlimited
    • Frequency Domain Formulation Unlimited
    • 1.1 Fourier Transforms and Delta Functions Unlimited
    • 1.2 Fourier Series and Time-Limited Functions Unlimited
    • 1.3 The Sampling Theorem Unlimited
    • 1.4 Discrete Observations Unlimited
    • 1.5 Aliasing Unlimited
    • 1.6 Discrete Fourier Analysis Unlimited
    • 1.7 Identities and Difference Equations Unlimited
    • 1.8 Circular Convolution Unlimited
    • 1.9 Fourier Series as Least-Squares Unlimited
    • 1.10 Stochastic Processes Unlimited
    • 1.11 Spectral Estimation Unlimited
    • 1.12 The Blackman-Tukey Method Unlimited
    • 1.13 Colored Processes Unlimited
    • 1.14 The Multitaper Idea Unlimited
    • 1.15 Spectral Peaks Unlimited
    • 1.16 Spectrograms Unlimited
    • 1.17 Effects of Timing Errors Unlimited
    • 1.18 Cross-Spectra and Coherence Unlimited
    • 1.19 Simulation Unlimited
    • Time Domain Methods Unlimited
    • 2.1 Representations-1 Unlimited
    • 2.2 Geometric Interpretation Unlimited
    • 2.3 Representations-2 Unlimited
    • 2.4 Spectral Estimation from ARMA Forms Unlimited
    • 2.5 Karhunen-Loève Theorem and Singular Spectrum Analysis Unlimited
    • 2.6 Wiener and Kalman Filters Unlimited
    • 2.7 Gauss-Markov Theorem Unlimited
    • 2.8 Trend Determination Unlimited
    • 2.9 EOFs, SVD Unlimited
    • Examples of Applications in Climate Unlimited
    • 3.1 References Unlimited

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Massachusetts Institute of Technology