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The phase of any wave is the temporally-initial (t = 0) displacement of the spatial point on the wave's medium serving as reference to all other points (x = 0). As independent variable "t" ticks forward, and independent variable "x" is surveyed in the positive and negative directions, sinusoidal/periodic variation of the wave's medium is observed. Image File history File links Broom_icon. ... Look up Phase in Wiktionary, the free dictionary Phase may refer to: Phase (matter), a physically distinctive form of a substance, such as the solid, liquid, and gaseous states of ordinary matter Phase (waves), the time position (or angle in the complex plane) within a cycle of a periodic waveform...

It is difficult to understand the concept of "phase" before considering the nature of a wave with zero phase. The wave's phase "shifts" forward or backward the wave's oscillations, relative to a wave with zero phase. This is best illustrated by the diagram contrasting in-phase waves (multiple waves have equal or nearly equal phases) and out-of-phase waves (multiple waves have a variety of phases).

In the context of periodic processes, phase can refer to:

Instantaneous phase

the present position in the cycle of something that changes cyclically

Phase shift

a constant difference/offset between two instantaneous phases, particularly when one is a standard reference

Waves are amplitudes that change cyclically, often modeled as sinusoidal functions of time (t) or some other variable. Consider the ever-changing angle: In signal processing, a general sinusoidal signal with constant amplitude can be defined as: where is the amplitude, and is the instantaneous phase (or local phase or simply phase) . The simplest useful form is: which is effectively the same as the cyclical form: , where mod is the Modulo_operation. ... This article is about waves in the most general scientific sense. ... Amplitude is a nonnegative scalar measure of a waves magnitude of oscillation, that is, magnitude of the maximum disturbance in the medium during one wave cycle. ... A sine wave or sinusoid is a waveform whose graph is identical to the generalized sine function y = Asin[ω(x − α)] + C where A is the amplitude, ω is the angular frequency (2π/P where P is the wavelength), α is the phase shift, and C is the vertical offset. ... Graph of example function, The mathematical concept of a function expresses the intuitive idea of deterministic dependence between two quantities, one of which is viewed as primary (the independent variable, argument of the function, or its input) and the other as secondary (the value of the function, or output). A...

and the amplitude wave:

where , , and are constants, and mod is the Modulo operation. In computing, the modulo operation finds the remainder of division of one number by another. ...

The initial phase (at t = 0) of this sinusoid is the initial angle , which is also commonly referred to as just "phase". The instantaneous phase at time is    which has units of radians.   has units of seconds, so has units of cycles per second (= 2π radians/sec = 360°/sec), which represents the frequency of the oscillations. Frequency is defined as the rate at which the instantaneous phase changes. The duration of one cycle of the wave, called its period, is given by:   (seconds per cycle). Some common angles, measured in radians. ... Look up second in Wiktionary, the free dictionary. ... The hertz (symbol: Hz) is the SI unit of frequency. ... A degree (in full, a degree of arc, arc degree, or arcdegree), usually symbolized °, is a measurement of plane angle, representing 1／360 of a full rotation. ... FreQuency is a music video game developed by Harmonix and published by SCEI. It was released in November 2001. ...

When is referred to as the phase or phase shift, the implied reference is:  .  For instance, that is what is meant by the "phase" of a Fourier transform at a particular frequency. The term "phase shift" also has a slightly more general usage, described in the next section. In mathematics, the Fourier transform is a certain linear operator that maps functions to other functions. ...

When the frequency of an oscillation is time invariant, time is sometimes used (instead of angle) to express instantaneous phase. Thus we measure the rotation of the earth in hours, instead of radians. Time zones are actually a good example of phase shifts. Other measures of phase are: (1) distance, and (2) fraction of the wavelength. The wavelength is the distance between repeating units of a wave pattern. ...

Phase shift

Illustration of phase shift. The horizontal axis represents an angle (phase) that is increasing with time.

Phase shifting describes relative phase shift in superimposing waves. Waves may be of electromagnetic (light, RF), acoustic (sound) or other nature. By superposing waves using different phase shifts the waves can add to (0° shift = "in phase") or cancel out each other (180°). Image File history File links Phase_shift. ... Image File history File links Phase_shift. ...

A phase shift is also a difference or change in the initial phase. If is delayed (time-shifted) by of its cycle, it becomes:

whose initial phase is   Thus, a shift in time is equivalent to a phase shift, for an infinitely long sinusoid. Conversely, a change in the initial phase is tantamount to a shift in time.

Phase difference

In-phase waves

Out-of-phase waves

Phase difference is similar to phase shift, but more likely to be applied in the context of two signals, particularly when neither is a standard reference. Two waves that have the same frequency and different initial phases have a phase difference that is constant (independent of time). So it is referred to simply as the phase difference, rather than the initial phase difference or the phase-shift difference. When the phase difference (modulo 2π) is zero, the waves are said to be in phase with each other. Otherwise, they are out of phase with each other. The terms are also commonly hyphenated, and used as an adjective:   "The out-of-phase signal caused distortion." If the phase difference is 180 degrees (π radians), then the two signals are said to be in antiphase. And if their peak amplitudes are equal, their sum is zero at all values of time, t. Image File history File links This is a lossless scalable vector image. ... Image File history File links This is a lossless scalable vector image. ... Image File history File links This is a lossless scalable vector image. ... Image File history File links This is a lossless scalable vector image. ... The word modulo (Latin, with respect to a modulus of ___) is the Latin ablative of modulus which itself means a small measure. ...

For input-output syastems, a phase lag would correspond to the output phase being radians less than the input phase. Phase lead is the phenomenom of the input phase being radians greater than the input phase. When the phases are in sequence, they are said to be at the resonant frequency.

In phase - this is analogous to two athletes running around a race track at the same speed and direction, side by side. They pass a point on the track together (simultaneously). Out of phase - this is analogous to two athletes running around a race track at the same speed and direction but starting at different positions on the track. They pass a point at different instants in time. But the time difference (phase difference) between them is a constant - same for every pass since they are at the same speed and in the same direction. If they were at different speeds, this would be analogous to two waves of different frequencies. Then, the phase (angle) difference measurement would be meaningless and void.

In-phase and quadrature components

Communication signals require more complicated forms (than above) of . The linear term is often extracted, and written separately, as follows:

where represents a carrier frequency, and Carrier frequency is the fundamental frequency used in both amplitude modulation and frequency modulation i. ...

and represent possible modulation of a pure carrier wave:    The modulation alters the original component of the carrier, and creates a (new) component, as shown above. The component that is in phase with the original carrier is referred to as the in-phase component. The other component, which is always 90° ( radians) "out of phase", is referred to as the quadrature component. In telecommunications, modulation is the process of varying a periodic waveform, i. ...

Phase coherence

Coherence is the quality of a wave to display well defined phase relationship in different regions of its domain of definition. Coherence is the property of wave-like states that enables them to exhibit interference. ...

In physics, quantum mechanics ascribes waves to physical objects. The wave function is complex and since its square modulus is associated to probability of observing the object, the complex character of the wave function is associated to the phase. Since the complex algebra is responsible for the striking interference effect of quantum mechanics, phase of particles is therefore ultimately related to their quantum behavior. Fig. ... A wave function is a mathematical tool that quantum mechanics uses to describe any physical system. ...

See also

• Instantaneous phase
• Frequency
• Phase cancellation
• Polarity
• Polarization

In signal processing, a general sinusoidal signal with constant amplitude can be defined as: where is the amplitude, and is the instantaneous phase (or local phase or simply phase) . The simplest useful form is: which is effectively the same as the cyclical form: , where mod is the Modulo_operation. ... FreQuency is a music video game developed by Harmonix and published by SCEI. It was released in November 2001. ... Phase cancellation refers to the effect of two waves that are out of phase with each other being summed. ... The polarity of an object is, in general, its physical alignment of atoms. ... In electrodynamics, polarization (also spelled polarisation) is the property of electromagnetic waves, such as light, that describes the direction of their transverse electric field. ...

External links

• Relationship of phase difference and time-delay