Zero-crossing rate

Template:Short description Template:Use dmy dates 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

$zcr=\frac{1}{T-1}\sum _{t=1}^{T-1}|\mathrm{s}\mathrm{g}\mathrm{n}[s(t)]-\mathrm{s}\mathrm{g}\mathrm{n}[s(t-1)]|$

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

$\mathrm{s}\mathrm{g}\mathrm{n}(x)=\{\begin{array}{l}1,x\ge 0\\ 0,x<0\end{array}$

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

• Zero crossing
• Digital signal processing

References

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