page_title: In-phase and quadrature components
section_title: Concept
hierarchical_section_title: In-phase and quadrature components / Concept
context_page_description: In electrical engineering, a sinusoid with angle modulation can be decomposed into, or synthesized from, two amplitude-modulated sinusoids that are offset in phase by one-quarter cycle. All three functions have the same center frequency. The amplitude modulated sinusoids are known as the in-phase and quadrature components.
  In some contexts it is more convenient to refer to only the amplitude modulation itself by those terms.
context_section_description: 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.   A phase-shift of x → x + π/2 changes the identity to:
  cos(x + φ) = cos(x) cos(φ) + cos(x + π/2) sin(φ),
  in which case cos(x) cos(φ) is the in-phase component.  In both conventions cos(φ) is the in-phase amplitude modulation, which explains why some authors refer to it as the actual in-phase component.
caption: IQ phasor diagram