How Smooth Do You Think I Am: An Analysis on the Frequency-Dependent Temporal Roughness of Velvet Noise

Velvet noise is a sparse pseudo-random signal, with applications in late reverberation modeling, decorrelation, speech generation, and extending signals. The temporal roughness of broadband velvet noise has been studied earlier. However, the frequency-dependency of the temporal roughness has little previous research. This paper explores which combinative qualities such as pulse density, filter type, and filter shape contribute to frequency-dependent temporal roughness. An adaptive perceptual test was conducted to find minimal densities of smooth noise at octave bands as well as corresponding lowpass bands. The results showed that the cutoff frequency of a lowpass filter as well as the center frequency of an octave filter is correlated with the perceived minimal density of smooth noise. When the lowpass filter with the lowest cutoff frequency, 125 Hz, was applied, the filtered velvet noise sounded smooth at an average of 725 pulses/s and an average of 401 pulses/s for octave filtered noise at a center frequency of 125 Hz. For the broadband velvet noise, the minimal density of smoothness was found to be at an average of 1554 pulses/s. The results of this paper are applicable in designing velvet-noise-based artificial reverberation with minimal pulse density.