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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?

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Under the assumption that your words "extract the amplitude of those four components" actually mean "extract the spectral magnitudes of those four components", then the initial phases of the original four periodic signals do not matter. It's straightforward to prove this behavior by modeling your down-conversion process using software.

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  • $\begingroup$ I had suspected this to be the case, but thank you for confirming it! Since I posted the question I've actually modeled it, as you suggest, and found that indeed I can extract the spectral magnitudes and phases in exactly the way I'd expect. $\endgroup$ – Ben S. Feb 19 at 20:51
  • $\begingroup$ @Ben S. Hi. Software modeling will answer most of our DSP questions. The problem with software modeling is that our software code does what we tell it to do rather than what we want it to do. $\endgroup$ – Richard Lyons Feb 20 at 10:58

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