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 zero to negative or from negative to zero to positive. 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

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

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, logically, between a pair of adjacent positive zero-crossings there must be one and only one negative zero-crossing.

For monophonic tonal signals, the zero-crossing rate can be used as a primitive pitch detection algorithm.

Applications

Zero crossing rates are used for Voice activity detection (VAD), i.e., finding whether human speech is present in an audio segment or not.

See also

• Zero crossing
• Digital signal processing