In-phase and quadrature components
mathematical technique for manipulating signals etc.
A sinusoid with modulation can be decomposed into, or synthesized from, two amplitude-modulated sinusoids that are in quadrature phase, i.e., with a phase offset of one-quarter cycle (90 degrees or π/2 radians). All three sinusoids have the same center frequency. 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.
Or in other words, it is possible to create an arbitrarily phase-shifted sine wave, by mixing together in different proportions two sine waves that are 90° out of phase.
The implication is that the modulations in some signal can be treated separately from the carrier wave of the signal. This has extensive use in many radio and signal processing applications. I/Q data is used to represent the modulations of some carrier, independent of that carrier's frequency.
Orthogonality
In vector analysis, a vector with polar coordinates A, φ and Cartesian coordinates x = A cos(φ), y = A sin(φ), can be represented as the sum of orthogonal components: [x, 0] + [0, y]. Similarly in trigonometry, the angle sum identity expresses:
sin(x + φ) = sin(x) cos(φ) + sin(x + π/2) sin(φ).
And in functional analysis, when x is a linear function of some variable, such as time, these components are sinusoids, and they are orthogonal functions.
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