From the trig identity
, we have
From this we may conclude that every sinusoid
can be expressed as the sum
of a sine function (phase zero) and a cosine function (phase
the sine part is called the ``in-phase'' component, the cosine part can be
called the ``phase-quadrature'' component. In general, ``phase
quadrature'' means ``90 degrees out of phase,'' i.e.
, a relative phase
It is also the case that every sum of an in-phase and quadrature component
can be expressed as a single sinusoid
at some amplitude and phase. The
proof is obtained by working the previous derivation backwards.
illustrates in-phase and quadrature components
overlaid. Note that they only differ by a relative
In-phase and quadrature sinusoidal components.
Next Section: Sinusoids at the Same FrequencyPrevious Section: Why Sinusoids are Important