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 | s g n [ s ( t ) ] − s g n [ s ( t − 1 ) ] | {\displaystyle zcr={\frac {1}{T-1}}\sum _{t=1}^{T-1}\left|\mathrm {sgn} [s(t)]-\mathrm {sgn} [s(t-1)]\right|}

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

s g n ( x ) = { 1 , x ≥ 0 0 , x < 0 {\displaystyle \mathrm {sgn} (x)={\begin{cases}1,\quad x\geq 0\\0,\quad x<0\end{cases}}}

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.