Radar maths I and Q components
Keep in mind that the value of fD can be positive or negative. The sign of fD has no effect on the I signal (cos(x) = cos(-x)), but it reverses the sign of the Q signal (sin(x) = -sin(-x)).

The 90&deg; phase shifter delays the Q signal &mdash; its output is Q90(t) = -sin(2&pi;fDt - &pi;/2) = cos(2&pi;fDt) when fD is positive, but it becomes
-cos(2&pi;fDt) when fD is negative.

Therefore, when fD is positive, the upper adder outputs cos(2&pi;fDt) - cos(2&pi;fDt) = 0, but when fD is negative, it outputs cos(2&pi;fDt) - (-cos(2&pi;fDt)) = 2 cos(2&pi;fDt).

Similarly, when fD is positive, the lower adder outputs cos(2&pi;fDt) + cos(2&pi;fDt) = 2 cos(2&pi;fDt), but when fD is negative, it outputs cos(2&pi;fDt) + (-cos(2&pi;fDt)) = 0.