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In Reply to: RE: Phase Distortion, dv/dt, and Slew Rate posted by Dave_K on December 18, 2015 at 13:57:41
Thanks for the analysis. I followed it (but am too rusty to do it).
I think you reinforced my argument. If you picture a bunch of voices (or instruments, or a mix) playing vibrato (or even just a little out of tune) then, while the probability of most of them lining up at a peak or valley is low at any one time, there are a hell of a lot of temporal opportunities (cycles) for that to happen. So I think it probably does happen, some, and the distribution of "slew-induced distortion events" would be predictable, and the intensity of such events would follow some kind of normal curve.
Thanks again for the insight and analysis. It helps.
The longer you sample, the greater the chance of a random collection of waves adding up and creating a large peak. Most recordings that are made cleanly (uncompressed and not subject to tape compression from loud recordings) will have a crest factor around 18 dB. With mild compression the crest factor will be around 15 dB. Percussive recordings can have much greater crest ratios, of course. Also, the recording style affects crest ratios, due to reverberations, etc.
These figures relate to short term period of averaging (0.5 to 2 seconds) during which the music is homogeneous. If you average over longer periods there will be occasional larger peaks and the possibility depends on the number of individual waveform sources. If musical dynamics come into play, then the crest factors can easily get to 25 dB or more.
If there is a rare peak over the ability of the recording or playback this may or may not be audible, depending on the technology. For example, momentary clipping of a stable amplifier on a percussive transient will not be audible if this happens infrequently in the course of a track. However, if the amplifier is unstable (i.e. incompetently designed) then a temporary overload on one peak may cause the amplifier to misbehave for an extended period. Similar problems happen with clipping in digital recording or playback. With LP playback peaks can cause needles to jump out of the groove, etc...
These are all factors well familiar to recording engineers, especially mastering engineers.
"Diversity is the law of nature; no two entities in this universe are uniform." - P.R. Sarkar
The math seems to indicate that the only waves which will add coherently are harmonics that are time aligned, i.e. harmonics from a single instrument or voice. The voices in a chorus will add incoherently, so the total acoustic power will be the sum of their individual acoustic powers.
Measurements of crest factor indicate that the pathological cases you're thinking of don't really happen, or at least they are so rare that they aren't a factor in recording. The highest observed crest factors are from impulses generated by percussive instruments, not from massed voices.
Anyway it's a moot point with modern solid state amplifiers because most are capable of slew rates faster than the product of their rail voltage and max frequency, which guarantees that they can't be driven into slew rate limiting with any input. That was not the case back in the 1970s when Walt Jung was writing about slew rate distortion, when amplifier slew rates were 1-2 orders of magnitude slower than today.
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