Relative Approach 2D / 3D

Relative Approach evaluates a sound the way a listener does: not by its absolute level, but by how much it deviates from what the ear expects. The analysis continuously predicts the level each frequency band should have, based on the recent history of that band and on its neighbouring bands, and then reports only the difference between the measured level and the predicted level. Steady background noise cancels out; impulses, tonal onsets, ticking, clicking and irregular structures stand out. This makes Relative Approach one of the most effective tools for finding a subjectively annoying component that is buried in a loud but uniform background.

Theory

Pattern Prediction and Residual

The signal is split into fractional-octave bands and each band is converted into a level-versus-time track. A regression (pattern) estimator runs along each track and produces a smooth prediction of the "expected" level. The output of the analysis is the residual — the part of the measured level that the estimator could not predict:

RA(t, f) = Level_measured(t, f) − Level_predicted(t, f)

A perfectly stationary sound is fully predictable, so its residual is close to zero regardless of how loud it is. A sound with a sudden onset or an isolated tonal component produces a large residual exactly where the irregularity occurs.

Pattern Directions

The prediction can be formed along the time axis, along the frequency axis, or along both. The choice determines which kind of irregularity is emphasised:

Time Pattern — predicts each band from its own recent history. Highlights temporal irregularities: impulses, rattle, ticking, onsets. This is the default.
Frequency Pattern — predicts each band from its spectral neighbours. Highlights spectral irregularities: isolated tones, whine, narrowband components standing out of a broadband background.
Frequency-Time Pattern — combines both directions, weighted by the Weighting F and Weighting T parameters.

Signal Chain

The channel is resampled to a common internal rate and a short fade-in is applied to avoid a start-up transient.
A fractional-octave filter bank splits the signal into bands (1/12 octave by default).
Each band level is smoothed with the selected time constant and decimated to the internal frame rate.
The regression estimator runs on the band matrix. The first fraction of a second is used to initialise the estimator and is not reported, so the result starts slightly after the beginning of the recording.
2D: the bands are combined into one curve. 3D: the band matrix is kept and reduced along time to the requested number of time values.

2D and 3D Variants

	Relative Approach 2D	Relative Approach 3D
Result type	Single curve versus time	Colour map, time × frequency band
How bands are combined	Energetic sum across all bands (one value per frame)	Not combined — every band is kept
Time resolution	Full internal frame rate	Reduced to Max Nbr of Time Values (peak per cell)
Unit	cPa	cPa
Typical use	Quick screening: when does something irregular happen	Diagnosis: when and at which frequency

The result unit cPa (centi-pascal, 10⁻² Pa) is a compressed pressure scale. Relative Approach values are not sound pressure levels and must not be compared with dB(SPL) figures — compare them only with other Relative Approach results.

Parameters

Parameter	Options / Range	Default	Description
Base Analysis	Filter nth Octave, FFT nth Octave, Loudness FFT	Filter nth Octave	How the band matrix is generated. The filter-bank variant follows the ear's time behaviour most closely.
Band Resolution	1/3, 1/6, 1/12, 1/24 octave	1/12 octave	Width of the analysis bands. Finer resolution separates close tones but increases computation time.
Spectral Weighting	None, A, B, C, D, G, and the vibration weightings Wb, Wc, Wd, We, Wf, Wh, Wj, Wk, Wm	None	Frequency weighting applied before the band analysis.
Time Constant F	s	0.005 s	Level smoothing used when the prediction runs along the frequency axis.
Time Constant T	s	0.005 s	Level smoothing used when the prediction runs along the time axis.
Variation Analysis	Regression, Prominence 3D	Regression	Method used to derive the deviation from the expected pattern.
Regression Algorithm	Time Pattern, Frequency Pattern, Frequency-Time Pattern	Time Pattern	Direction of the prediction (see above).
Weighting F	0 – 1	0.5	Share of the frequency-direction prediction in the combined algorithm.
Weighting T	0 – 1	0.5	Share of the time-direction prediction in the combined algorithm.
Max Nbr of Time Values	integer (3D only)	600	Number of columns in the colour map. Each column holds the maximum of the frames it covers, so short events are never lost by the reduction.

Reading the Result

Values near zero mean "as expected" — predictable, and therefore subjectively unobtrusive.
Peaks mark the moments (2D) or the time/frequency cells (3D) that a listener perceives as standing out. Use a cursor to read off the exact time and, in 3D, the band centre frequency.
Because the estimator needs a short warm-up, the curve does not start exactly at t = 0. Keep this in mind when the event of interest is right at the beginning of a recording — record a little lead-in.
The single value shown in the footer summarises the curve or map and is useful for pass/fail limits and for comparing variants of the same product.

Typical Applications

Locating ticking, clicking or knocking in an otherwise smooth engine or e-drive run-up.
Finding relay, actuator and latch noises inside a loud ambient recording.
Assessing rattling and squeaking of interior trim during a road or shaker test.
Detecting an intermittent bearing or gear defect that a long-term averaged spectrum hides.
Quantifying how much a design change reduces the "noticeability" of a defect, not just its level.

Practical Tips

Start with the defaults (Filter nth Octave, 1/12 octave, Time Pattern). They match the classic Relative Approach behaviour and are the right starting point for impulsive problems.
Switch to Frequency Pattern when the complaint is a tone or whine rather than an impulse.
Run 2D first for a quick overview of when something happens, then run 3D on the same data to see where in frequency it happens.
A shorter time constant makes the analysis more sensitive to very short impulses; a longer one suppresses them and emphasises slower modulations.
Feed the analysis with the unfiltered recording. Applying a strong band filter beforehand removes the spectral context the prediction relies on.

Relative Approach deliberately suppresses stationary content. A component that is loud but perfectly steady will produce a small Relative Approach value. Never use this analysis on its own to judge overall loudness — combine it with a level or loudness analysis.