adamdea;578793 Wrote: > I have been studying this quite carefully as there are lots of useful > points. I promise it wasn't point 1 I was missing and I don't think it > was point 3 although I guess I do find the terms resolution and > precision confusing. (I have been puzzling over the question of what > the precision of an analogue system is) > > I also undertake never to allow my mind to wander into visual > analogies. > What I am getting confused about is what happens when a sound (which, > obviously as you point out, has an amplitude that varies over time)gets > louder and softer. Let's assume there is no other sound in the > recording. If the sound (is it allowed to be a sine wave?) varies in > amplitude between 128 and 32- xxx...10000000 and xxxx....00100000 > and it became louder so that the peak amplitude was 2048 > xxx....100000000000, what would be the number which now represents the > minimum amplitude of this wave? Would it be 1952 (11110100000 ?) or > something else? > I have a feeling that if I could grasp this I could understand the > point.
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 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) -- Phil Leigh You want to see the signal path BEFORE it gets onto a CD/vinyl...it ain't what you'd call minimal... Touch(wired/XP) - TACT 2.2X (Linear PSU) + Good Vibrations S/W - MF Triplethreat(Audiocom full mods) - Linn 5103 - Aktiv 5.1 system (6x LK140's, ESPEK/TRIKAN/KATAN/SEIZMIK 10.5), Pekin Tuner, Townsend Supertweeters, Blue Jeans Digital,Kimber Speaker & Chord Interconnect cables Kitchen Boom, Outdoors: SB Radio, Harmony One remote for everything. ------------------------------------------------------------------------ Phil Leigh's Profile: http://forums.slimdevices.com/member.php?userid=85 View this thread: http://forums.slimdevices.com/showthread.php?t=82050 _______________________________________________ audiophiles mailing list [email protected] http://lists.slimdevices.com/mailman/listinfo/audiophiles
