My input is a single signal composed of the sum of four periodic signals, each 4 Hz apart, centered around some resonant f0 typically between 1200 - 1300 Hz; the actual frequencies will change occasionally, but not the distance between them. For example, if f0=1250, my frequencies will be [f1..f4] = 1244, 1248, 1252, and 1256 Hz.
A decent analogy would be four LEDs flashing at these frequencies, observed by a single detector.
This signal is sampled at 16384 Hz, and I perform IQ demodulation in software (described here) using the [f1..f4] as the reference frequencies to ultimately extract the amplitude of those four components from the original signal.
My question is about the phases of the four different components. I can control their phases, and I'm wondering if there are any best practices to make sure I get the cleanest possible separation of the four signals, or if the phase won't matter?