Re: [LAD] FULL audio-signal path

On Sun, Jul 22, 2007 at 01:29:19PM -0400, Paul Davis wrote: I did a quick experiment. N floating point signals, all of them Gaussian distributed, summed both as single and double precision. If the difference between the two sums is considered 'noise', the signal/noise ratios R in dB are: N R ---------------- 16 -142.9 32 -140.0 64 -136.7 128 -133.8 256 -130.7 512 -128.0 1024 -124.7 2048 -121.9 4096 -118.8 So even when summing 1024 signals the result is better than 120 dB, and an already big mixing session with 64 sources would produce 136 dB. This should be compared to the S/N ratio of individual sources which is unlikely to be better than 90 or 100 dB. The only case where things would turn out to be worse is when you are mixing signals that cancel systematically and the resulting low level sum is amplified. If that happens you will have other and much more serious problems anyway. And it's quite easy to improve these figures even when using just single precision. For example if the summing is done in two steps, first making sums of 4 inputs and then adding these, the results for large N improves by 6 dB: N R ---------------- 16 -146.2 32 -144.2 64 -141.8 128 -139.3 256 -136.6 512 -133.6 1024 -130.7 2048 -127.8 4096 -124.9 Or 12 dB using a first grouping of 16: N R ---------------- 16 -142.3 32 -141.8 64 -141.3 128 -140.4 256 -139.3 512 -137.5 1024 -135.7 2048 -133.2 4096 -130.6 Or two intermediate levels of 4: N R ---------------- 16 -144.8 32 -143.9 64 -143.1 128 -141.8 256 -140.4 512 -138.3 1024 -135.9 2048 -133.6 4096 -130.5 Taking this to the limit, a binary tree addition would produce the best results. This also explains why even single-precision FFTs produce good results when used for convolution - an FFT computes sums over all its input samples, but the addition is organised as a tree by the very nature of the algorithm. -- FA Follie! Follie! Delirio vano è questo !