zero-crossing rate

{{Short description|Rate which a signal changes from positive to negative or negative to positive.}}

{{Use dmy dates|date=February 2015}}

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.* Chen, C. H., Signal processing handbook, Dekker, New York, 1988 Its value has been widely used in both speech recognition and music information retrieval, being a key feature to classify percussive sounds.Gouyon F., Pachet F., Delerue O. (2000),[https://web.archive.org/web/20181029191653/https://pdfs.semanticscholar.org/6509/14f8be2c96ab2f55faec54d3e3876c5b1b69.pdf 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.

ZCR is defined formally as

:$zcr\; =\; \backslash frac\{1\}\{T-1\}\backslash sum\_\{t=1\}^\{T-1\}\backslash left|\; \backslash mathrm\{sgn\}[s(t)]-\backslash mathrm\{sgn\}[s(t-1)]\backslash right|$

where $s$ is a signal of length $T$ and $\backslash mathrm\{sgn\}(x)$ is a sign function defined as:

:

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.