personally, i believe this issue is resolved with the choice of the window size (or "frame length", not to be conflated with "frame hop") that goes into the FFT. for a sufficiently large window, the two sinusoids will appear as two separate peaks in the FFT result. for a sufficiently small window, it will be a single sinusoid, but the amplitude will vary in adjacent windows. that's my spin on the issue. r b-j ---------------------------- Original Message ---------------------------- Subject: Re: [music-dsp] two fundamental questions Re: FFT for realtime synthesis? From: "gm" <[email protected]> Date: Sat, November 3, 2018 2:12 am To: [email protected] -------------------------------------------------------------------------- > > And I think you can model them simply by adding their phasors/bins/numbers... > > for opposite angles they will cancel, for the same angle they will be > amplified > > so the model is correct at the center of the window, but it models just > an instance in time and spreads this instance > > in this way of thinking you basically consider the dft a sine bank > oscillator > > > Am 03.11.2018 um 05:59 schrieb Ross Bencina: >> On 3/11/2018 3:41 AM, Ethan Fenn wrote: >>> No length of FFT will distinguish between a mixture of these sine >>> waves and a single amplitude-modulated one, because they're >>> mathematically identitical! Specifically: >>> >>> sin(440t) + sin(441t) = 2*cos(0.5t)*sin(440.5t) >>> >>> So the question isn't whether an algorithm can distinguish between >>> them but rather which one of these two interpretations it should >>> pick. And I would say in most audio applications the best answer is >>> that it should pick the same interpretation that the human hearing >>> system would. In this example it's clearly the right-hand side. In >>> the case of a large separation (e.g. 440Hz and 550Hz, a major third) >>> it's clearly the left-hand side. And somewhere in between I guess it >>> must be a toss-up. >> >> I guess you could model both simultaneously, with some kind of >> probability weighting. >> >> Ross. > > � � � -- r b-j� � � � � � � � � � � � �[email protected] "Imagination is more important than knowledge." � � � �
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