Yes, you don't really want 32 octaves. Wide bandwidth becomes a problem with 1/f noise because the lower frequencies are so much higher amplitude than the upper frequencies. With 32 bit floats and a 24 bit mantissa you can only represent 24 octaves of 1/f noise because 1/f = 1/(2^24) drops below the quantization limit. This means the top 8 octaves of your 32 cannot be represented.
Let's assume you want a high sampling rate, say 384 kHz (the problem only gets worse if you lower the sample rate). Nyquist is 192 kHz. 32 octaves below that is 0.0000447 Hz, or 1 cycle every 3.86 days.. The amplitude at 20 Hz of the noise will be 20*log10(2^(20/0.0000447)) = -113 dB below the amplitude of the lowest octave. Your signal will be dominated by subsonic audio and the audio range will be below the threshold of hearing. On Mon, Apr 11, 2016 at 10:46 AM, robert bristow-johnson < r...@audioimagination.com> wrote: > being that this is a discussion group about music, which is a subset of > audio. and being that our hearing is at best 10 or 11 octaves, why do you > need 32 octaves? > > and then how closely, in dB, does your pink noise need to conform to the > 1/f power spectrum? +/- 0.1 dB? 0.01 dB? > > all this can be done with a good white noise source and a filter > alternating real poles and real zeros placed at just the right values. for > 32 octaves, i would hate to guess how many pole/zero pairs you would need. > maybe 10. > > > > r b-j > > > ---------------------------- Original Message ---------------------------- > Subject: [music-dsp] High quality really broad bandwidth pinknoise > (ideally more than 32 octaves) > From: "Seth Nickell" <snick...@gmail.com> > Date: Mon, April 11, 2016 12:57 pm > To: music-dsp@music.columbia.edu > -------------------------------------------------------------------------- > > > > I'm applying an iterative function to an input signal, in this instance > > pinknoise. Because of the iteration, spectral characteristics in input > > signals tend to "blow up" really quickly, so I'm looking for a really > high > > bandwidth and high quality source of pink noise. > > > > My understanding is that most of the approaches like the supercollider > > PinkNoise.ar ugen are mostly accurate, but over a limited bandwidth. As > the > > number of octaves grows, the accurcary drops. Is my understanding > correct? > > > > I'm hoping to find a way to generate pink noise that is: > > 1) Accurate over an arbitrarily wide bandwidth, at least 32 octaves > > 2) Tractable to generate an arbitrarily large number of samples > (billions, > > so can't fft the whole thing in one pass) > > > > Any suggestions? I've read through > > http://www.firstpr.com.au/dsp/pink-noise/#Pseudo, but everyone seems > > focused on fast-generation of pink noise of moderate quality and a > > relatively narrow bandwidth. I'm sort of looking for the other side of > > things... what's the most ideal pink noise I can generate en masse? > > > > Thanks, > > -Seth > > > -- > > r b-j r...@audioimagination.com > > "Imagination is more important than knowledge." > > > > _______________________________________________ > dupswapdrop: music-dsp mailing list > music-dsp@music.columbia.edu > https://lists.columbia.edu/mailman/listinfo/music-dsp > -- --- james mccartney
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