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Phase comparison is a comparison of the phase of two waveforms, usually of the same nominal frequency. In time and frequency, the purpose of a phase comparison is generally to determine the frequency offset (difference between signal cycles) with respect to a reference. [3]
Instantaneous phase and frequency are important concepts in signal processing that occur in the context of the representation and analysis of time-varying functions. [1] The instantaneous phase (also known as local phase or simply phase ) of a complex-valued function s ( t ), is the real-valued function:
The period and frequency are determined by the size of the mass m and the force constant k, while the amplitude and phase are determined by the starting position and velocity. The velocity and acceleration of a simple harmonic oscillator oscillate with the same frequency as the position, but with shifted phases. The velocity is maximal for zero ...
The phase velocity of a wave is the rate at which the wave propagates in any medium. This is the velocity at which the phase of any one frequency component of the wave travels. For such a component, any given phase of the wave (for example, the crest) will appear to travel at the phase velocity.
In signal processing and electronics, the frequency response of a system is the quantitative measure of the magnitude and phase of the output as a function of input frequency. [1] The frequency response is widely used in the design and analysis of systems, such as audio and control systems , where they simplify mathematical analysis by ...
where ν is the frequency of the wave, λ is the wavelength, ω = 2πν is the angular frequency of the wave, and v p is the phase velocity of the wave. The dependence of the wavenumber on the frequency (or more commonly the frequency on the wavenumber) is known as a dispersion relation.
The peak amplitude and the frequency of the carrier signal are maintained constant, but as the amplitude of the message signal changes, the phase of the carrier changes correspondingly. Phase modulation is an integral part of many digital transmission coding schemes that underlie a wide range of technologies like Wi-Fi, GSM and satellite ...
Even in dispersive media, the frequency f of a sinusoidal wave is equal to the phase velocity v of the wave divided by the wavelength λ of the wave: =. In the special case of electromagnetic waves in vacuum , then v = c , where c is the speed of light in vacuum, and this expression becomes f = c λ . {\displaystyle f={\frac {c}{\lambda }}.}