Initial algebra

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. 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

$zcr=\frac{1}{T-1}\sum _{t=1}^{T-1}\mathbb{𝕀}\left\{s_t{s}_{t-1}<0\right\}$

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

• Zero crossing
• Digital signal processing

References

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