On Tue, Nov 30, 2010 at 3:50 AM, Element Green <jgr...@users.sourceforge.net> wrote: > I hadn't given this much thought and just assumed a linear cross fade > (0-100%) would be the way to do it
I'll try to elucidate with two extreme examples. If the signal is white noise, then a linear cross-fade will make a dip in the volume, centered at the cross fade. This is because the phases of the two signals (one being faded in an one being faded out) don't match and there will be partial cancellation of components of the signal. On average the phase difference will be 90 deg. I recall my frustration using a sample editor which only offered linear cross-fade. It would often create this kind of a dip. The other example: If the signal is sinusoidal, then you can adjust the loop length to obtain a perfect match. In this case the linear cross fade will work perfectly: It does nothing, as the signals are already identical around the loop points. For uncorrelated signals you'd like to use something like this instead of a linear cross fade, to compensate for the dip: x = 0..1 is the time position inside the cross-fade f(x) is the gain function for the signal that is being faded in f(1-x) is the gain function for the signal that is being faded out These constraints should be satisfied: f(0) = 0 f(1) = 1 f(x)^2 + f(1-x)^2 = 1 The last constraint above normalizes power or amplitude for the mixture of uncorrelated signals. Some functions that are applicable: f(x) = sqrt(x) f(x) = sin(pi/2*x) f(x) = x/sqrt(x^2+(1-x)^2) The last one is probably my favorite, as it has the same gain ratio f(x)/f(1-x) as a linear cross fade. It doesn't start the fade in as abruptly as the others. This is quite a similar problem as finding a nice pan law. -olli -- dupswapdrop -- the music-dsp mailing list and website: subscription info, FAQ, source code archive, list archive, book reviews, dsp links http://music.columbia.edu/cmc/music-dsp http://music.columbia.edu/mailman/listinfo/music-dsp
