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The satellite carrier's total phase can be measured with ambiguity regarding the number of cycles. Let ϕ i , j , k {\displaystyle \phi _{i,j,k}} denote the phase of the carrier of satellite j {\displaystyle j} measured by receiver i {\displaystyle i} at time t k {\displaystyle t_{k}} .
As described in the previous section, the range to a satellite is essentially calculated by multiplying the carrier wavelength times the number of whole cycles between the satellite and the rover and adding the phase difference. Determining the number of cycles is non-trivial, since signals may be shifted in phase by one or more cycles.
If the phase-offset/delay of the multiply-filter-divide system is known, it can be compensated for to recover the correct phase. In practice, applying this phase compensation is complicated. [4] In general, the modulation's order matches the nonlinear operator required to produce a clean carrier harmonic. As an example, consider a BPSK signal.
Phasor notation (also known as angle notation) is a mathematical notation used in electronics engineering and electrical engineering.A vector whose polar coordinates are magnitude and angle is written . [13] can represent either the vector (, ) or the complex number + =, according to Euler's formula with =, both of which have magnitudes of 1.
The two amplitude-modulated sinusoids are known as the in-phase (I) and quadrature (Q) components, which describes their relationships with the amplitude- and phase-modulated carrier. [ A ] [ 2 ] Or in other words, it is possible to create an arbitrarily phase-shifted sine wave, by mixing together two sine waves that are 90° out of phase in ...
The carrier-envelope phase (CEP) or carrier-envelope offset (CEO) phase is an important feature of an ultrashort laser pulse and gains significance with decreasing pulse duration, in a regime where the pulse consists of a few wavelengths. Physical effects depending on the carrier-envelope phase fall into the category of highly nonlinear optics.
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