Weighted 1/3-Octave Analysis for Sound and Human Vibration

Raw physical data shows the instrument's view, while people, regulations and contracts use a human view. Weighting converts the first into the second, and the module makes the switch a single selection.

The problem it solves

A weighted spectrum describes the measured vibration or sound during the selected analysis period. Occupational exposure assessment also requires representative sampling, exposure duration, the required axis combination and the applicable regulation. A current-frame weighted RMS or dB value alone does not establish daily exposure or compliance.

Functions

Hand-held tool vibration exposure (ISO 5349)

Handle vibration of drills, angle grinders, breakers and rock drills is weighted with Wh. The combined weighted vibration magnitude ahv is an input to the daily exposure calculation A(8), together with the duration of each task. Compare the duration-normalized result with the applicable occupational regulation; ISO 5349 is a measurement and evaluation method, not a universal exposure limit.

Ride comfort of vehicles and machinery (ISO 2631)

Seat vibration can be evaluated using whole-body Wk (vertical) or Wd (horizontal) weighting. Comfort and occupational health assessments use different criteria. Daily exposure assessment also requires exposure duration and the axis factors and method specified for the task; the current weighted RMS alone is insufficient.

Product noise and compliance (dBA)

A-weighted sound pressure is used in many product and environmental specifications. For example, a hypothetical refrigerator contract might specify 45 dBA under stated test conditions; that is not a universal product limit. C-weighting retains more low-frequency energy and may be used for peak assessments when required. With the 20 µPa reference, the module displays dBA or dBC.

Acoustic calibration and measurement chain check

A sound calibrator at 1 kHz and 94 dB checks the measurement chain at that frequency. A- and C-weighting are nominally 0 dB at 1 kHz, so the three readings should be close to the calibrator value within the applicable tolerances. This single-point check does not validate full-band response or instrument conformity.

Micro-vibration and special measurements

Vibration on precision instrument foundations or lithography platforms can be below 1 µm/s², where normal unit readings are long strings of zeros. Converted to dB with a 1 µm/s² (or 0.1 µg) reference, the reading becomes a two-digit number; velocity (1 nm/s) and displacement references are also available. References for underwater sound (1 µPa) and for sound intensity and sound power (ISO 1683) are included.

Electronics and audio engineering

With the dBV (1 V), dBu (0.775 V) or dBm (1 mW) reference, the same spectrum engine analyzes audio equipment levels and power in frequency bands.

The calculation has four steps: divide into bands, sum energy, apply the standard weighting, and combine the total level.

Step 1: FFT spectrum and window correction

Each frame is windowed with a Hanning window and transformed by FFT. Windowing loses energy, so the software applies the amplitude correction (× 2) and the energy correction (× √(8/3)), so band energies match the true values. If this step is wrong, all later dB values are systematically low.

Step 2: 1/3-octave band energy

The 1/3-octave scale doubles the frequency every three bands; each band is bounded by its center frequency multiplied or divided by 2^(1/6). By Parseval's theorem, the band RMS is the square root of the sum of squared RMS values of all FFT lines in the band. The peak spectrum is divided by √2 to give RMS, and the band edges are limited to the actual analysis range (resolution to upper analysis frequency). This also explains why white noise rises by 3 dB per octave in an octave spectrum while pink noise is flat: higher bands contain more lines.

Step 3: band-by-band weighting

Each weighting curve is a table of dB corrections per band defined by the standard; the software multiplies each band by the linear factor 10^(dB/20).

When a weighting is selected, the displayed band range changes accordingly (for example 10 Hz–16 kHz for A and C, 6.3 Hz–1.6 kHz for hand-arm and 0.5–80 Hz for whole-body) and components outside it are not counted.

Step 4: total RMS and total weighted level

Total RMS = √(Σ weighted band RMS²) Total level = 20 · lg(total RMS / 0 dB reference)

In contour mode the total level is the energy sum of the band levels, 10 · lg Σ 10^(band dB / 10); the two methods are equivalent and cross-check each other. The 0 dB references follow international conventions: 20 µPa for airborne sound (threshold of hearing), 1 µm/s² for micro-vibration and 1 nm/s for velocity. A dB value is relative and has meaning only with its reference.

Stable readings: exponential averaging

Spectra fluctuate from frame to frame during live measurement. Exponential averaging (new data weighted 1/N into the history) converges quickly while still following changes. The number of averages is 1–1000; restart the average after changing the operating condition.

Quick reference: weighting and reference

Measured data on channel 2, read in four steps: total level, spectral shape, bands, conclusion.

1. Total level first: the example display reads 137.86 dB. Its interpretation requires the selected weighting, reference, physical unit and analysis period; the number alone cannot establish exposure or compliance.
2. Spectral shape: the bands from 31.5 to 200 Hz are clearly higher than the rest (about 128–130 dB), so the energy is concentrated at low and mid frequencies. From 315 Hz the bands fall and stay at about 57–60 dB, so high-frequency content is weak. This points to the nature of the source, such as unbalance, resonance or gear mesh.
3. Compare weightings: with A-weighting the low-frequency bands are reduced strongly and the total level drops noticeably — the difference between physically loud and loud to the ear. With hand-arm weighting for a hand-held tool, the low- and mid-frequency bands are reduced far less than with A-weighting, and they dominate the total.
4. Conclusion: identify the dominant bands and record the weighted magnitude, reference and measurement conditions. For an exposure assessment, include the task durations and required normalization before comparison with the applicable criterion. This illustrative spectrum does not establish a health pass or fail.