Zero-crossing rate
# Zero-crossing rate

The zero-crossing rate (ZCR) is the rate at which a signal changes from positive to zero to negative or from negative to zero to positive. Its value has been widely used in both speech recognition and music information retrieval, being a key feature to classify percussive sounds.

ZCR is defined formally as

    $zcr={\frac {1}{T-1}}\sum _{t=1}^{T-1}\mathbb {1} _{\mathbb {R} _{<0}}(s_{t}s_{t-1})$

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

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

For monophonic tonal signals, the zero-crossing rate can be used as a primitive pitch detection algorithm. Zero crossing rates are also used for Voice activity detection (VAD), which determines whether human speech is present in an audio segment or not.

