Expressed in Fourier space, the multiplication formula_106 is a convolution of their Fourier transforms formula_107 and formula_108. The positive feedback arises because the formula_109 component of formula_28 converts the formula_111 component of formula_33 into a driving signal at formula_113, and vice versa (reverse the signs). This explains why the pumping frequency must be near formula_114, twice the natural frequency of the oscillator. Pumping at a grossly different frequency would not couple (i.e., provide mutual positive feedback) between the formula_111 and formula_113 components of formula_33.