Generalizations of Velvet Noise and their Use in 1-Bit Music
A family of spectrally-flat noise sequences called “Velvet Noise” have found use in reverb modeling, decorrelation, speech synthesis, and abstract sound synthesis. These noise sequences are ternary—they consist of only the values −1, 0, and +1. They are also sparse in time, with pulse density being their main design parameter, and at typical audio sampling rates need only several thousand non-zero samples per second to sound “smooth.” This paper proposes “Crushed Velvet Noise” (CVN) generalizations to the classic family of Velvet Noise sequences including “Original Velvet Noise” (OVN), “Additive Random Noise” (ARN), and “Totally Random Noise” (TRN). In these generalizations, the probability of getting a positive or negative impulse is a free parameter. Manipulating this probability gives Crushed OVN and ARN low-shelf spectra rather than the flat spectra of standard Velvet Noise, while the spectrum of Crushed TRN is still flat. This new family of noise sequences is still ternary and sparse in time. However, pulse density now controls the shelf cutoff frequency, and the distribution of polarities controls the shelf depth. Crushed Velvet Noise sequences with pulses of only a single polarity are particularly useful in a niche style of music called “1- bit music”: music with a binary waveform consisting of only 0s and 1s. We propose Crushed Velvet Noise as a valuable tool in 1- bit music composition, where its sparsity allows for good approximations to operations, such as addition, which are impossible for signals in general in the 1-bit domain.