Zero-crossing rate

The zero-crossing rate (ZCR) is the rate at which a <a href="/facts/Signal_(information_theory)/41YqUJ8c">signal</a> changes from positive to zero to negative or from negative to zero to positive. Its value has been widely used in both <a href="/facts/Speech_recognition/z7S7Pgk6">speech recognition</a> and <a href="/facts/Music_information_retrieval/6QH7SpSo">music information retrieval</a>, 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 <a href="/facts/Monaural/1lKJ5jAW">monophonic</a> tonal signals, the zero-crossing rate can be used as a primitive <a href="/facts/Pitch_detection_algorithm/BE4EBmrv">pitch detection algorithm</a>. Zero crossing rates are also used for <a href="/facts/Voice_activity_detection/qbCG12fE">Voice activity detection</a> (VAD), which determines whether human speech is present in an audio segment or not.

Zero-crossing rate open-in-new

Zero-crossing rate