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.