Overview
ISO 18431-2:2004 - "Mechanical vibration and shock - Signal processing - Part 2: Time domain windows for Fourier Transform analysis" specifies the algebraic functions for a selected set of time-domain window functions used to pre‑process digitally sampled vibration and shock data before Discrete Fourier Transform (DFT/FFT) spectral analysis. The standard defines the commonly used Hanning, flat‑top, and rectangular windows and provides examples showing their effects on amplitude and spectral leakage.
Key topics
- Window function definitions
- Hanning: w(ν) = 1 − cos(2πν/N), ν = 0..N−1 - a tapered window that reduces sidelobes.
- Flat‑top: w(n) = 1 + a1 cos(2πn/N) + a2 cos(4πn/N) + a3 cos(6πn/N) + a4 cos(8πn/N) with coefficients:
- a1 = −1.933, a2 = +1.286, a3 = −0.388, a4 = +0.0322 - optimized for accurate amplitude measurement.
- Rectangular: w(n) = 1 - the no‑window case (included for completeness).
- Performance trade‑offs
- Amplitude accuracy vs. frequency resolution: flat‑top gives best amplitude accuracy (useful for calibration); rectangular gives best frequency resolution; Hanning is a compromise.
- Spectral leakage and equivalent noise bandwidth: the document discusses how window choice influences leakage and noise bandwidth.
- Examples and illustrations
- Worked examples applying each window to truncated and non‑truncated sinusoidal signals show differences in amplitude error and noise bandwidth.
- Normative reference
- ISO 2041 (vibration and shock vocabulary) is cited for terms and definitions.
Applications
ISO 18431-2 is directly applicable to engineers and practitioners working on:
- Vibration and shock measurement and analysis (acceleration, velocity, displacement)
- FFT/DFT spectral analysis in condition monitoring, modal testing, NVH (noise, vibration & harshness), and calibration laboratories
- Data preprocessing in signal processing toolchains where window selection affects spectral estimates, amplitude accuracy, and sideband identification
Who uses it:
- Test engineers, vibration analysts, calibration labs, acoustic/NVH specialists, and software developers implementing DFT/FFT routines for instrumentation and measurement systems.
Related standards
- ISO 18431-1: General introduction (part of the same series)
- Other parts in the ISO 18431 series (time–frequency methods and shock response analysis) are noted in the standard as under preparation.
- ISO 2041:1990 - Vibration and shock - Vocabulary (normative reference)
Keywords: ISO 18431-2, time domain windows, Hanning window, flat-top window, rectangular window, Fourier Transform, DFT, FFT, vibration and shock, spectral leakage, window functions, equivalent noise bandwidth.
Open preview (PDF)Mechanical vibration and shock — Signal processing — Part 2: Time domain windows for Fourier Transform analysis