Zero crossing
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A zero-crossing is a point where the sign of a
mathematical function In mathematics, a function from a set (mathematics), set to a set assigns to each element of exactly one element of .; the words ''map'', ''mapping'', ''transformation'', ''correspondence'', and ''operator'' are sometimes used synonymously. ...
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, mathematics,
acoustics Acoustics is a branch of physics that deals with the study of mechanical waves in gases, liquids, and solids including topics such as vibration, sound, ultrasound and infrasound. A scientist who works in the field of acoustics is an acoustician ...
, and
image processing An image or picture is a visual representation. An image can be two-dimensional, such as a drawing, painting, or photograph, or three-dimensional, such as a carving or sculpture. Images may be displayed through other media, including a pr ...
.


In electronics

In
alternating current Alternating current (AC) is an electric current that periodically reverses direction and changes its magnitude continuously with time, in contrast to direct current (DC), which flows only in one direction. Alternating current is the form in w ...
, the zero-crossing is the instantaneous point at which there is no
voltage Voltage, also known as (electrical) potential difference, electric pressure, or electric tension, is the difference in electric potential between two points. In a Electrostatics, static electric field, it corresponds to the Work (electrical), ...
present. In a
sine wave A sine wave, sinusoidal wave, or sinusoid (symbol: ∿) is a periodic function, periodic wave whose waveform (shape) is the trigonometric function, trigonometric sine, sine function. In mechanics, as a linear motion over time, this is ''simple ...
or other simple waveform, this normally occurs twice during each cycle. It is a device for detecting the point where the voltage crosses zero in either direction. The zero-crossing is important for systems that send
digital data Digital data, in information theory and information systems, is information represented as a string of Discrete mathematics, discrete symbols, each of which can take on one of only a finite number of values from some alphabet (formal languages ...
over AC circuits, such as
modem The Democratic Movement (, ; MoDem ) is a centre to centre-right political party in France, whose main ideological trends are liberalism and Christian democracy, and that is characterised by a strong pro-Europeanist stance. MoDem was establis ...
s, X10 home automation
control system A control system manages, commands, directs, or regulates the behavior of other devices or systems using control loops. It can range from a single home heating controller using a thermostat controlling a domestic boiler to large industrial ...
s, and Digital Command Control type systems for Lionel and other AC model trains. Counting zero-crossings is also a method used in speech processing to estimate the
fundamental frequency The fundamental frequency, often referred to simply as the ''fundamental'' (abbreviated as 0 or 1 ), is defined as the lowest frequency of a Periodic signal, periodic waveform. In music, the fundamental is the musical pitch (music), pitch of a n ...
of speech. In a system where an amplifier with digitally controlled gain is applied to an input signal, artifacts in the non-zero output signal occur when the gain of the amplifier is abruptly switched between its discrete gain settings. At audio frequencies, such as in modern consumer electronics like digital audio players, these effects are clearly audible, resulting in a 'zipping' sound when rapidly ramping the gain or a soft 'click' when a single gain change is made. Artifacts are disconcerting and clearly not desirable. If changes are made only at zero-crossings of the input signal, then no matter how the amplifier gain setting changes, the output also remains at zero, thereby minimizing the change. (The instantaneous change in gain will still produce distortion, but it will not produce a click.) If electrical power is to be switched, no electrical interference is generated if switched at an instant when there is no current—a zero crossing. Early light dimmers and similar devices generated interference; later versions were designed to switch at the zero crossing.


In signal processing

In the field of digital
image processing An image or picture is a visual representation. An image can be two-dimensional, such as a drawing, painting, or photograph, or three-dimensional, such as a carving or sculpture. Images may be displayed through other media, including a pr ...
, great emphasis is placed on operators that seek out edges within an image. They are called '' edge detection'' or ''gradient filters''. A gradient filter is a filter that seeks out areas of rapid change in pixel value. These points usually mark an edge or a boundary. A Laplace filter is a filter that fits in this family, though it sets about the task in a different way. It seeks out points in the signal stream where the digital signal of an image passes through a pre-set '0' value, and marks this out as a potential edge point. Because the signal has crossed through the point of zero, it is called a zero-crossing. An example can be foun
here
including the source in Java. In the field of industrial radiography, it is used as a simple method for the segmentation of potential defects. In the field of NLP, the rate of zero crossings observed in a
spectrogram A spectrogram is a visual representation of the spectrum of frequencies of a signal as it varies with time. When applied to an audio signal, spectrograms are sometimes called sonographs, voiceprints, or voicegrams. When the data are represen ...
can be used to distinguish between certain phonemes such as fricatives, voiceless stops, and vowels.


See also

* Reconstruction from zero crossings * Zero crossing control * Zero-crossing rate * Zero of a function (a root) *
Sign function In mathematics, the sign function or signum function (from '' signum'', Latin for "sign") is a function that has the value , or according to whether the sign of a given real number is positive or negative, or the given number is itself zer ...


References

{{reflist Signal processing