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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 1 R < 0 ( s t s t − 1 ) {\displaystyle zcr={\frac {1}{T-1}}\sum _{t=1}^{T-1}\mathbb {1} _{\mathbb {R} _{<0}}(s_{t}s_{t-1})} where s {\displaystyle s} is a signal of length T {\displaystyle T} and 1 R < 0 {\displaystyle \mathbb {1} _{\mathbb {R} _{<0}}} is an indicator function. 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.
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