In an ideal I/Q modulator or demodulator, the I channel is mixed with cos(2Ï€ 2*π*fLO*t), while the Q channel is mixed with -sin(2Ï€ 2*π* fLO*t):
Using the identity:
cos(fLO) = cos(s)Â·cos(t) - sin(s)Â·sin(t)
We can relate -sin(2Ï€fLOt) to cos(2Ï€fLOt2*π*fLO*t) to cos(2*π*fLO*t) by:
cos(fLO + Ï€π/2) = cos(fLO)Â·cos(Ï€π/2) - sin(fLO)Â·sin(Ï€π/2) = -sin(fLO)
Therefore, applying a 90 degree phase shift to cos(2Ï€fLOt2*π*fLO*t) is identical to -sin(2Ï€fLO 2*π*fLO*t).