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What does the expression 'combine signals coherently' imply?

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It means that they are in phase---think of the signals as waves. Adding noncoherent signals results in cancellation, or fading.

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    $\begingroup$ I agree with your first sentence, but the second is not necessarily true. Non-coherence sometimes results in destructive interference, but not always. There are, in fact, demodulation techniques for signals like FSK that can be done non-coherently. They just don't work as well as the coherent methods. $\endgroup$
    – Jim Clay
    May 3, 2012 at 20:29
  • $\begingroup$ So adding signals coherently implicitly implies that the signals are of same frequency? $\endgroup$
    – sauravrt
    May 5, 2012 at 2:12
  • $\begingroup$ Yes. Generally you can consider the coherence along the spectrum; at one frequency the signals may be coherent, and not at another. Thanks to Jim for the amendment. $\endgroup$
    – Emre
    May 5, 2012 at 2:33
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It means to combine signals taking phase into account (with respect to some mutually related reference point). Taking phase into account allows signals to sum when in phase, or cancel when out of phase (with respect to that related reference point).

For instance, when summing the result vectors of successive FFT frames together, you can just add the magnitudes, which would be an incoherent combination, or sum the complex vectors, which would give you a coherent sum. With the coherent combination, any stationary sinusoids with a frequency exactly between 2 FFT bins across 2 successive FFT frames would cancel out instead of summing its spectrum, thus better rejecting that spectrum if it is undesired.

In the time domain, it might mean adjusting the phase of a PLL to match that of an estimate of some carrier's phase, so that a signal combination maintains some coherent relative phase relationship, instead of the relative phase being yet another unknown into some modulation, demodulation or detection process.

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  • $\begingroup$ hotpaw2, Perhaps I have misunderstood you in the 2nd paragraph, however I do not think that adding 2 (complex) FFT bins together (i.e, two phasors of different phases) constitutes a coherent sum. For it to be coherent, the phasors would have to be alligned, (thus, same phase). That being said, I agree with the rest of your post. $\endgroup$
    – Spacey
    May 3, 2012 at 21:15
  • $\begingroup$ @Mohammed : Disagree. Active cancellation requires a phase coherent process. $\endgroup$
    – hotpaw2
    May 3, 2012 at 21:21
  • $\begingroup$ Yes, it is a phase-coherent process - but how is adding two phasors that are not phase-coherent (ie, not same phase) 'phase coherent' to begin with? Let us say a phasor of magnitude 1 and phase 0 degrees is added to a phasor of magnitude 1 and phase 180 degrees. The result is 0 - an incoherent sum. If it was coherent sum, the phases would be alligned/rotated, and our sum would be 2. $\endgroup$
    – Spacey
    May 3, 2012 at 21:25

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