Riddle: what is this waveform, and what does it *sound* like? I knew what the answer was going to be, but it surprised me anyway.pic.twitter.com/024W9LWsqh
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Okay, so
@jix got it first without spoiling it too much, and@datenwolf said it out loud. The answer is that it sounds exactly the same as a square wave, because it is a square wave, with every frequency component phase shifted by 90 degrees.Show this thread
So take the Hilbert transform, or multiply every component of the (positive/real) FFT by i.
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Thanks. Twitter will use this to make your timeline better. UndoUndo
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Now I riddle this to you: Assume that you have a detector that can only detect |𝓕(y(t))|, i.e. only the power spectrum with the phase lost: What can you do to the signal before it hits the detector to recover the phase? You may also use multiple detectors.
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You need to encode phase into something else, which means you need a phase reference to relate all the phases to... I'm thinking modulate with a quadrature carrier pair is going to be part of this?
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This is the correct answer (Hilbert transform of a square wave). I think the previous one (square wave with every frequency component shifted 90 degrees) was not accurate...
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... unless you also apply a different scale to each 90 degree shifted frequency component (that the Hilbert transform does).
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