In Reply to: RE: 20-bit processing posted by Todd Krieger on July 14, 2009 at 19:47:20:
No, I don't think that's right. Imagine doing a sequence of arithmetic operations and rounding to a resolution of 0.001 every time:
The right answer, rounded to the nearest 0.001, is 1.250. But if you round to the nearest 0.001 at each step then you'll end up with a value of 1.000 -- an error 250 times greater than your resolution of 0.001.
- X = 4.001 (the original value)
- X = X / 4
- X = X - 1
- X = X * 1000
- X = X + 1
But if instead you rounded to the nearest 0.00001 at every intermediate step, and then rounded the final answer to the nearest 0.001, you'll get the right answer of 1.250.
This, apparently, is what the 20 bits were for, to provide an extra 4 bits of resolution for the intermediate values of the arithmetic computations. The starting value (the quantized analog sample) and the final value (the number put on the CD) may only be 16 bits, just like in the example above the starting and final values are rounded to the nearest 0.001. But you must have more resolution for internal arithmetic manipulation or else there could be a severe degree of error in the final numbers put on CD.
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Follow Ups
- RE: 20-bit processing - ephemere 07/14/0921:25:22 07/14/09 (33)
- RE: 20-bit processing - Todd Krieger 23:06:49 07/14/09 (32)
- RE: 20-bit processing - J. Phelan 01:03:22 07/15/09 (31)
- RE: 20-bit processing - Todd Krieger 01:14:16 07/15/09 (30)
- RE: 20-bit processing - J. Phelan 01:37:18 07/15/09 (29)
- RE: 20-bit processing - Todd Krieger 11:38:27 07/15/09 (28)
- RE: 20-bit processing - J. Phelan 17:45:07 07/15/09 (27)
- RE: 20-bit processing - Todd Krieger 23:56:02 07/15/09 (26)
- RE: 20-bit processing - J. Phelan 00:56:26 07/16/09 (25)
- RE: 20-bit processing - Todd Krieger 18:39:20 07/16/09 (0)
- RE: 20-bit processing - Tony Lauck 10:10:05 07/16/09 (23)
- RE: 20-bit processing - J. Phelan 12:39:52 07/16/09 (22)
- RE: 20-bit processing - Tony Lauck 13:51:03 07/16/09 (21)
- RE: 20-bit processing - J. Phelan 15:31:50 07/16/09 (20)
- RE: 20-bit processing - Todd Krieger 18:55:11 07/16/09 (1)
- RE: 20-bit processing - J. Phelan 19:09:31 07/16/09 (0)
- RE: 20-bit processing - Tony Lauck 17:48:57 07/16/09 (17)
- RE: 20-bit processing - Werner 01:21:17 07/17/09 (1)
- Why 32 bit converters - Tony Lauck 08:31:03 07/17/09 (0)
- RE: 20-bit processing - J. Phelan 18:02:57 07/16/09 (14)
- RE: 20-bit processing - Todd Krieger 19:18:11 07/16/09 (0)
- RE: 20-bit processing - DaveK 18:27:01 07/16/09 (12)
- RE: 20-bit processing - J. Phelan 19:05:48 07/16/09 (6)
- RE: 20-bit processing - DaveK 20:39:33 07/16/09 (5)
- RE: 20-bit processing - J. Phelan 21:11:17 07/16/09 (4)
- RE: 20-bit processing - DaveK 21:39:57 07/16/09 (3)
- RE: 20-bit processing - J. Phelan 22:20:39 07/16/09 (2)
- RE: 20-bit processing - Tony Lauck 19:55:26 07/17/09 (1)
- RE: 20-bit processing - J. Phelan 20:17:18 07/17/09 (0)
- RE: 20-bit processing - Tony Lauck 18:47:12 07/16/09 (4)
- RE: 20-bit processing - J. Phelan 19:12:41 07/16/09 (3)
- Many others ? - Metralla 04:26:22 07/17/09 (2)
- RE: Many others ? - J. Phelan 05:45:14 07/17/09 (1)
- RE: Many others ? - Tony Lauck 20:49:38 07/17/09 (0)