10 Vibration Signal Analysis Clarence W. de Silva

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The University of British Columbia

10.1 Introduction ........................................................................ 10-1

10.2 Frequency Spectrum ........................................................... 10-2

Frequency † Amplitude Spectrum † Phase Angle †

Phasor Representation of Harmonic Signals † RMS

Amplitude Spectrum † One-Sided and Two-Sided

Spectra † Complex Spectrum

10.3 Signal Types ......................................................................... 10-7

10.4 Fourier Analysis .................................................................. 10-7

Fourier Integral Transform † Fourier Series Expansion

† Discrete Fourier Transform † Aliasing Distortion †

Another Illustration of Aliasing

10.5 Analysis of Random Signals ............................................... 10-18

Ergodic Random Signals † Correlation and Spectral

Density † Frequency Response Using Digital Fourier

Transform † Leakage (Truncation Error) † Coherence

† Parseval’s Theorem † Window Functions † Spectral

Approach to Process Monitoring † Cepstrum

10.6 Other Topics of Signal Analysis ......................................... 10-26

Bandwidth † Transmission Level of a Band-Pass Filter

† Effective Noise Bandwidth † Half-Power (or 3 dB)

Bandwidth † Fourier Analysis Bandwidth † Resolution

in Digital Fourier Results

10.7 Overlapped Processing ....................................................... 10-28

Order Analysis

Summary

This chapter considers the nature and analysis of vibration signals. Both time-domain techniques and frequencydomain

techniques are investigated, which are related through Fourier transform. Topics covered include signal

types, signal sampling, aliasing error, truncation error, window functions, spectral analysis, bandwidth issues, and

order analysis. Several applications of signal analysis in mechanical vibration are discussed.

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