Mechanical Engineering 434, Random Data and Spectral Analysis

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Catalog description

Introduction to analysis of random data: stationarity, ergodicity, probability density function and related statistics, spectral desnity function, autocorrelation, and crossing analysis. Applying spectral analysis: fast Fourier transform, aliasing, zero-padding, and excitation-response characteristcs. Nonstationary data and spectral analysis.

Prerequisite: None.

Who takes it

Real world data is often random in its nature rather than deterministic. Even deterministic data is often buried in a noisy signal. A great variety of tools exist to handle these problems. Most have a fundamental basis in spectral analysis. This course is ideal for students interested in extracting information from their measurements, applying correlations or spectral analysis, and understanding the basis for more advanced data analysis techniques such as wavelet transforms or cepstral analysis. The analysis tools discussed in this course are pertinent for many disciplines including vibrations, turbulence, tribology, nondestructive testing, acoustics, and signal processing.

What it's about

ME 434 provides a solid background in the basics of signal processing and how to apply various signal processing techniques.

Lectures:

The course meets two days per week for 90-minute lectures or three days per week for 1-hour lectures. Topics include:

  • Introduction to random data analysis
    • Deterministic vs. random data
    • Ergodicity
    • Stationarity
  • Probability
    • Probability density function
    • Expected value (mean, standard deviation, skewness, flatness)
    • Joint probability density function
    • Gaussian distribution
    • Parameter estimation
  • Correlations
    • Autocorrelation
    • Cross-correlation
    • Two-dimensional correlation
  • Spectral Analysis
    • Fourier series and integrals
    • Autospectral density
    • Narrow band and broad band processes
    • Cross-spectral density
    • Discrete Fourier transform
    • Methods of measuring spectra
    • Spectra for discrete data
  • Implementation of spectral analysis for discrete data
    • Sampling and aliasing
    • Fast Fourier transform
    • Windowing
    • Zero padding
    • Error
  • Excitation-response systems
    • Input/output relationships
    • Impulse-response method
    • Frequency response
    • Excitation-response for stationary systems
    • Response to white noise input
    • Coherence
    • Filtering
  • Miscellaneous topics (some topics may not be covered)
    • Waterfall displays
    • Non-stationary data analysis
    • Cepstral analysis
    • Decomposition of a time-space wave field
    • Wavelet analysis
    • Modal analysis
    • Crossing analysis

Assignments/Evaluation:

Assignments/evaluations will include programming, homework, final project, and a mid-term exam.

Textbook:

An Introduction to Random Vibrations, Spectral, and Wavelet Analysis by D. E. Newland, Longman 1993

Contact:

Professor: Richard Lueptow
e-mail: r-lueptow@northwestern.edu