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How Smooth Do You Think I Am: an analysis on the frequency-dependent temporal roughness of velvet-noise

Jade Roberts, Jon Fagerström, Sebastian J. Schlecht and Vesa Välimäki

Companion page for the paper "How Smooth Do You Think I Am: an analysis on the frequency-dependent temporal roughness of velvet-noise" accepted for DAFx2023, Copenhagen, Denmark.


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 with a median of 668 pulses/s and a median of 290 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 a median of 1587 pulses/s. The results of this paper are applicable in designing velvet-noise-based artificial reverberation with minimal pulse density.

Filtered Velvet Noise

Second-order lowpass filtered velvet noise and fourth-order octave filtered velvet noise sound examples. Multi Track Audio Player

Broadband vs. Filtered Velvet Noise

Broadband Noise

Lowpass Filtered Noise

Octave Filtered Noise