Phase-sensitive detection ($X=A\cos \varphi ,Y=A\sin \varphi$)

phase-sensitive detection correlates an input with a synchronized reference and filters the product. Sinusoidal quadrature references recover both signal amplitude and relative phase. Narrow detection bandwidth rejects incoherent noise but cannot reject a background coherent at the same frequency; changing the integration time also changes settling and tracking speed.^[ref]