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suppose you take a signal, and duplicate it, then apply a low pass and high pass filter both with the same frequency and roll-off respectively to each signal, then combine the two signals additively, will that be a good approximate for the original signal? (guessing from some experimentation in audacity, this seems to be true of white noise at least)

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As long as you have identical rolloff characteristics - slope and frequency, the mix of the two will be identical to the original signal.

Whether the filter alters phase or not depends entirely on the design of the filter. For instance a basic first order R/C filter will alter the phase by between 45 and 90 degrees depending on slope and frequency. There are many different filter designs which can be emulated by IIR/FIR filters in the digital domain.

As far as frequency and level go, you're good to go.

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  • I guess this would be the principle of a speaker crossover [not that I know what design elements they may use to prevent phase-shift.] – Tetsujin May 13 at 8:26
  • This is an interesting article that explains phase in passive R/C Filter networks. electronics-tutorials.ws/filter/filter_2.html – Mark May 14 at 7:24
  • We are however starting to sidestep into the realms of the electronics stack. Would suggest also to the OP that they could also get a meaningful answer to this question on both the electronics and the dsp stack sites. Would be interesting to see the crosspost and how the perspective of the answer differs. – Mark May 14 at 7:26
  • Judging by the way I tested this in audacity, the specific filters it uses don't alter phase, as when I combined the two waveforms, subtracting with the original waveform left behind only quiet minor 'glitches' in the waveform. – micsthepick May 14 at 12:23
  • @Mark I was considering whether I should post on Electronics or this site, and I settled for this one – micsthepick May 14 at 12:24

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