Velvet noise is a sparse ternary pseudo‐random signal containing only a small portion of non‐zero values. In this work, the derivation of the spectral properties of velvet noise is presented. In particular, it is shown that the original velvet noise is white, i.e. has a constant power spectrum. For velvet noise variants with altered probability of polarity, the spectral characteristics are analytically derived. Crushed additive velvet noise is shown to have potential in the design of coloured sparse noise sequences, which are useful in acoustic signal processing.