The zero-crossing rate (ZCR) is the rate at which a
signal
In signal processing, a signal is a function that conveys information about a phenomenon. Any quantity that can vary over space or time can be used as a signal to share messages between observers. The '' IEEE Transactions on Signal Processing' ...
changes from positive to zero to negative or from negative to zero to positive. Its value has been widely used in both
speech recognition
Speech recognition is an interdisciplinary subfield of computer science and computational linguistics that develops methodologies and technologies that enable the recognition and translation of spoken language into text by computers with the ma ...
and
music information retrieval
Music information retrieval (MIR) is the interdisciplinary science of retrieving information from music. MIR is a small but growing field of research with many real-world applications. Those involved in MIR may have a background in academic musico ...
, being a key feature to classify percussive sounds.
[Gouyon F., Pachet F., Delerue O. (2000]
On the Use of Zero-crossing Rate for an Application of Classification of Percussive Sounds
in ''Proceedings of the COST G-6 Conference on Digital Audio Effects (DAFX-00 - DAFX-06), Verona, Italy, December 7–9, 2000''. Accessed 26 April 2011.
ZCR is defined formally as
:
where
is a signal of length
and
is an
indicator function
In mathematics, an indicator function or a characteristic function of a subset of a set is a function that maps elements of the subset to one, and all other elements to zero. That is, if is a subset of some set , one has \mathbf_(x)=1 if x ...
.
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
Monaural or monophonic sound reproduction (often shortened to mono) is sound intended to be heard as if it were emanating from one position. This contrasts with stereophonic sound or ''stereo'', which uses two separate audio channels to reproduc ...
tonal signals, the zero-crossing rate can be used as a primitive
pitch detection algorithm
Pitch may refer to:
Acoustic frequency
* Pitch (music), the perceived frequency of sound including "definite pitch" and "indefinite pitch"
** Absolute pitch or "perfect pitch"
** Pitch class, a set of all pitches that are a whole number of octav ...
. 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
A zero-crossing is a point where the sign of a mathematical function changes (e.g. from positive to negative), represented by an intercept of the axis (zero value) in the graph of the function. It is a commonly used term in electronics, mathemat ...
*
Digital signal processing
Digital signal processing (DSP) is the use of digital processing, such as by computers or more specialized digital signal processors, to perform a wide variety of signal processing operations. The digital signals processed in this manner ar ...
References
Signal processing
Rates
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