Zero-crossing rate

The zero-crossing rate is the rate of sign-changes along a signal, i.e., the rate at which the signal changes from positive to negative or back. This feature has been used heavily in both speech recognition and music information retrieval, being a key feature to classify percussive sounds.

ZCR is defined formally as

where ${\displaystyle s}$ is a signal of length ${\displaystyle T}$ and ${\displaystyle \mathbb {1} _{\mathbb {R} _{<0}}}$ is an indicator function.

In some cases only the "positive-going" or "negative-going" crossings are counted, rather than all the crossings - since, logically, between a pair of adjacent positive zero-crossings there must be one and only one negative zero-crossing.

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