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Zero-crossing rate

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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

z c r = 1 T − 1 ∑ t = 1 T − 1 1 R < 0 ( s t s t − 1 ) {\displaystyle zcr={\frac {1}{T-1}}\sum _{t=1}^{T-1}\mathbb {1} _{\mathbb {R} _{<0}}(s_{t}s_{t-1})}

where s {\displaystyle s} is a signal of length T {\displaystyle T} and 1 R < 0 {\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 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.

See also

References

  1. * Chen, C. H., Signal processing handbook, Dekker, New York, 1988
  2. Gouyon F., Pachet F., Delerue O. (2000),On the Use of Zero-crossing Rate for an Application of Classification of Percussive Sounds, in Proceedings of the COST G-6 Conference on Digital Audio Effects (DAFX-00 - DAFX-06), Verona, Italy, December 7–9, 2000. Accessed 26 April 2011.


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