Roughness Analysis

Roughness describes the perception of rapid amplitude modulations in a sound. When a carrier signal is modulated at rates between approximately 15 Hz and 300 Hz, listeners perceive a characteristic "rough" or "buzzing" quality. Maximum roughness sensation occurs at a modulation frequency of about 70 Hz. Roughness is an important sound quality metric for evaluating engine noise, gear whine, electric motor tones, and power-tool sounds.

Theory

Amplitude Modulation Detection

The auditory system detects amplitude modulation (AM) within each critical band. The roughness model applies a bank of critical-band filters to the input signal, computes the envelope of each band output, and extracts the modulation depth and modulation frequency. Only modulations within the roughness-relevant range (15 – 300 Hz) contribute to the result.

Modulation Depth

The modulation depth m describes the ratio of envelope fluctuation amplitude to the mean envelope level:

m = (E_max − E_min) / (E_max + E_min)

A fully modulated signal (100% AM) has m = 1.0 and produces maximum roughness at the optimal modulation frequency.

Roughness Model

The total roughness is calculated by summing the modulation-depth contributions across all critical bands, weighted by a modulation-frequency transfer function f_mod that peaks at approximately 70 Hz:

R = k · Σ_i f_mod(f_m,i) · m_i² · Δz_i [asper]

The constant k is calibrated so that a 1 kHz tone with 100% AM at 70 Hz and 60 dB SPL yields exactly 1 asper.

Parameters

Parameter	Options	Description
Block Size	40 ms – 200 ms	Analysis window length; shorter blocks improve temporal resolution at the cost of reduced modulation frequency resolution
Overlap	0% – 75%	Overlap between consecutive analysis blocks
Modulation Frequency Range	15 Hz – 300 Hz (fixed)	Band-pass range for modulation detection; not user-adjustable
Field Type	Free field / Diffuse field	Ear transfer function for the underlying critical-band analysis

Output Quantities

Quantity	Unit	Description
R	asper	Overall roughness value
R'(z)	asper/Bark	Specific roughness spectrum showing the contribution of each critical band
R(t)	asper	Roughness vs Time trace for time-varying signals

Specific Roughness

The specific roughness spectrum R'(z) reveals which frequency regions contribute most to the overall roughness. This is invaluable for diagnostic purposes: a peak in specific roughness around 16 Bark, for example, indicates modulated energy near 3 – 4 kHz, which could correspond to gear-mesh frequency interactions or electric motor commutation effects.

Roughness vs Time

The time-varying roughness R(t) is computed on a block-by-block basis. This allows tracking of roughness evolution during transient events such as:

Engine acceleration where gear-mesh modulation varies with RPM
Electric motor start-up with changing commutation patterns
Brake squeal events with intermittent modulated tonal components

Interpretation Guidelines

Reference value: 1 asper is defined as the roughness of a 1 kHz tone at 60 dB SPL, 100% amplitude-modulated at 70 Hz.

< 0.2 asper — Smooth; no perceptible roughness.
0.2 – 0.5 asper — Slight roughness; may be acceptable depending on product context.
0.5 – 1.0 asper — Moderate roughness; typically noticeable and possibly objectionable in vehicle interiors.
> 1.0 asper — Strong roughness; clearly perceptible buzzing or harsh character.

Practical Application Notes

Roughness is closely related to the perception of "harshness" in automotive NVH. Engine orders that produce modulation near 70 Hz at certain RPM ranges will create roughness peaks in run-up tests.
Electric vehicle (EV) motors can produce significant roughness due to PWM switching frequencies that create AM sidebands around the motor tones.
To reduce roughness in a product, the root-cause modulation source must be identified. The specific roughness spectrum helps localize the critical frequency band.
Roughness and fluctuation strength address the same phenomenon (temporal modulation) but at different modulation rates. Ensure the correct metric is selected based on the modulation frequency of interest.

Standard References

P. Daniel & R. Weber, "Psychoacoustical Roughness: Implementation of an Optimized Model," Acustica / acta acustica, vol. 83, 1997
E. Zwicker & H. Fastl, Psychoacoustics: Facts and Models, 3rd ed., Springer, 2007, Chapter 11: Roughness
W. Aures, "Ein Berechnungsverfahren der Rauhigkeit," Acustica, vol. 58, 1985