Roughness Model and Computation

Roughness, like fluctuation strength, is a sensation induced by signal fluctuations.

In Sound: Analysis and Specification, the roughness model is based on Daniel and R Weber’s paper, Psychoacoustical roughness: implementation of an optimized model, Acta Acustica united with Acustica, 83:113-123 (1997). It involves the following steps:

  • The signal is decomposed in consecutive frames (200-ms Blackman window, 50% overlap).

  • In each frame, the signal is filtered to take into account the effect of the outer and middle ear, and further spectrally decomposed over the Bark scale.

  • The signal in each Bark band is then filtered by a bandpass filter, generally centered at 70 Hz, but whose precise shape depends on the Bark band under consideration.

  • A generalized modulation depth mi* is calculated in each band by dividing the rms value of the signal output by the filter by its DC-value and only values above one are further considered.

  • A weighting is applied to the obtained generalized modulation depth in each Bark band. The weighting function tends to favor modulation depth in the bands roughly between 7 and 15 Barks.

  • The weighted modulation depths are then multiplied by the cross-correlation factors obtained between the signal envelopes in adjacent Bark Bands.

  • The results of these multiplications are finally added together and multiplied by a calibration factor set to obtain the reference value of one asper for a 100% amplitude-modulated one-kHz pure tone at 60 dB SPL, with a modulation frequency of 70 Hz.

  • The final overall roughness value corresponds to the median roughness value over time.