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.[1] This feature has been used heavily in both speech recognition and music information retrieval, being a key feature to classify percussive sounds.[2]

ZCR is defined formally as

zcr = \frac{1}{T-1} \sum_{t=1}^{T-1} {{\mathbb I}\left\{{s_t s_{t-1} < 0}\right\}}

where s is a signal of length T and the indicator function {{\mathbb I}\left\{{A}\right\}} is 1 if its argument A is true and 0 otherwise.

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 a segment of speech is voiced or unvoiced.

See also

References

  1. ↑
    • Chen, C. H., Signal processing handbook, Dekker, New York, 1988
  2. ↑ Gouyon F., Pachet F., Delerue O. (2000),Classifying percussive sounds: a matter of zero-crossing rate?, in Proceedings of the COST G-6 Conference on Digital Audio Effects (DAFX-00), Verona, Italy, December 7–9, 2000. Accessed 26 April 2011.