Phil Leigh;578811 Wrote: > OK - I'll try, but only if you promise to stop with the photography > analogies :-) > > 1) all sound can be represented by the summation of a series of sine > wives (Fourier) - so yes, the simplest sound is a pure sine wave. > However, lets use a triangle wave instead to keep the maths simpler > > 2) To keep it simple, lets use 4 bits instead of 16 so the max decimal > value is 15 and the min is 0, with the "zero-crossing point" being 8 (8 > = silence) > > 3) so, a fixed frequency triangle wave (say 1kHz) sampled at a sampling > frequency of 13kHz (so you get 13 samples per wavelength) could be: > > 8 10 12 14 12 10 8 6 4 2 4 6 8 > That would be very loud. > if we reduced the level by 6dB we'd get: > > 8 9 11 13 11 9 8 7 5 3 5 7 8 > You can see that the level (wave amplitude) has been "reduced" by "1 > bit" at each sampling point except at the zero crossing point of the > waveform (you can't have "less than zero"). > > But look - we started with 8 10 12 14, now we have 8 9 11 13 - our nice > triangle slope is distorted! we wanted to go 8 9.5 11 12.5 - but we > can't!!! > > This neatly illustrates the problem with recording in 4-bits!... you > get the idea - now we have insufficient precision to record the correct > value so we have to choose... Whatever we choose will be wrong... > > More bits = bigger numbers = more precision in the sample values = > smaller errors when capture them AND if we change the numbers later. > > in binary the two sequences would be: > 8 10 12 14 12 10 8 6 4 2 4 6 8 > 8421 > ---- > 1000 > 1010 > 1100 > 1110 > 1100 > 1010 > 1000 > 0110 > 0100 > 0010 > 0100 > 0110 > 1000 > > changed to: > 8 9 11 13 11 9 8 7 5 3 5 7 8 > 8421 > ---- > 1000 > 1001 > 1011 > 1101 > 1011 > 1001 > 1000 > 0111 > 0101 > 0011 > 0101 > 0111 > 1000 > > > > Does this help? Maybe it's the "zero-crossing" issue that's throwing > you? > I've used 4 bits here to exaggerate the issue. As you increase the > number of bits available, the "rounding error" problem diminishes - you > get increasingly precise numbers at each sample point... and if you > perform any kind of DSP - which always involves floating point maths - > on fixed precision numbers you get errors. More bits=smaller errors. > > OK - I'll let you have a photo analogy now :-) > bits in audio (representation of amplitude) are similar to bits in > photography (representation of contrast/hue). Less bits = less > gradation of contrast and less pallete range. 1 bit = pure black & > white (or a full scale pure square wave in audio whose only variable is > the mark/space ratio) Do you realize what you might have started? Such a bad/good person. Time will tell.
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