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\subsection{Quadrature Noise}  The motion of a Harmonic Oscillator can be described in phasespace - a point in phase  space, together with the time-evolution equations completely determines i.e.  the motion of the oscillator. However, due to noise, it's impossible to determine this point exactly - there's an amount of uncertainty as to where exactly coordinates that define  the system are its position and momentum in time. In normalized phase space, for a harmonic  oscillator is the points only differ  in phase space. and the curve follows a perfect circle.  A point in phase space, together with the time-evolution equations completely determines the motion of the oscillator, however, due to noise, it's impossible to determine this point exactly - there's an amount of uncertainty as to where exactly the oscillator is in phase space.  The same analysis can be applied to signals - suppose we have some signal $f(t)$, the signal can be written in the same  form \[f(t) = X(t) cos(\omega t) + Y(t) sin(\omega t)\]