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Digital Drive Upsamplers, DACs, jitter, shakes and analogue withdrawals, this is it. |
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Digital Drive Upsamplers, DACs, jitter, shakes and analogue withdrawals, this is it. |
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In Reply to: I Stand Corrected........ posted by Todd Krieger on July 15, 2009 at 00:40:36:
Here's a simple example of noise shaping. Suppose that you quantize a number (say it was 0.5) but it was rounded down to 0. The result is noise in the amount of -0.5. If this error is fed back (negative feedback) into the next sample, which we will assume is also 0.5, the resulting sum, 1.0 will be rounded to 1. The residual error to carry forward will be 0. If the signal sits at DC, then the output will be a steady stream of 0101010101, and the result will be no noise at DC, but a lot of noise at period 2. The noise has been shaped.
Now this simplistic example shows one of the problems with noise shaping, namely limit-cycle behavior. This can be broken by adding randomness, i.e. dither, but now things get more complicated. The dither noise itself has to be shaped as well, unless it can be subtracted out at the very end. Proper dither linearizes the quantization and removes the limit cycles, which come from a non-linear system with feedback.
If you really have to understand how all this works, then read the attached link. It provides a comprehensive explanation, both to/from analog and from one digital bit depth to another. Caution: Tough Mathematics! Note that this thesis does not explain how 1 bit DSD works. Not surprising, because 1 bit delta-sigma modulation does not actually work properly, being sufficiently non-linear to preclude any rational analysis. (If you doubt this, read the user's manual for the Weiss Saracon conversion software, and how there is special klugery to fix "latch up".)
Noise shaping in systems with a 44.1 kHz sampling rate are of marginal value, as the noise is moved from one audible frequency to another slightly less audible frequency. Noise shaping works much better with higher sampling rates, where the noise can be moved to frequencies that are octaves above the audible range.
Tony Lauck
"Diversity is the law of nature; no two entities in this universe are uniform." - P.R. Sarkar
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Follow Ups
- A very simple example of noise shaping - Tony Lauck 07/17/0914:54:57 07/17/09 (0)
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