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Maximum slew rate typically found in music/voice

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CatalinaWOW:
All of this discussion is wrapped around amplifier design and the effect of slew rate on distortion etc.

I have had an interest in slew rate for a different reason.  I transcribe old LPs (and other recordings) to .mp3 for convenience in listening and to avoid the problems controlling dirt, wear and other things in mechanical media.  I am not an audiophoole, and in fact with my old ears don't need particularly hi-fi.  But would like to remove the ticks, pops and clicks from the vinyl.  The automatic click removal tool in Audacity actually does yeoman work in removing the highest amplitude clicks.  But if it's parameters are adjusted to get rid of all of the audible clicks it has a noticeable negative impact to the sound, even to my pedestrian ears.

You can manually go through the recording and eliminate the rest, but it is incredibly tedious and if the record is particularly noisy it can take many hours.  Hence I started to write my own automatic click detector.  Slew rate is an obvious metric, so many clicks have a slew rate easily within the recording equipment's capability, but out of family for the music on the record (and probably all music, since the stuff I am listening to has cymbal strikes and other similar sounds).  But I never came up with a meaningful result.  Partly because I found that the psychoacoustic stuff was too complex for me.  You could have two clicks with identical time traces and one would be painfully audible and another inaudible even with careful listening depending on the sounds surrounding them in time.  Many clicks that were objectionable had lower slew rates than "real" sounds.

Long diatribe, with the only point being that slew rate may have other impacts than on the purity of reproduction.

mzzj:

--- Quote from: HalFoster on September 16, 2023, 12:29:29 am ---
I really wasn't looking to get too complicated with this, I just thought that someone, somewhere, would have done this research and might have published it somewhere. 

Hal

--- End quote ---
See my link above earlier.. " The prize for greatest slew rate found goes to a single peak from 'Year 3000' by Busted, which hit 150mV, equivalent to the slew rate of a full level sine wave about 10kHz, i.e. five times greater than Baxandall's figure, and equivalent to a level of 2.5V/µsec for a 100W power level."

https://www.renardson-audio.com/slew-tid.html

David Hess:

--- Quote from: wraper on September 15, 2023, 09:48:54 pm ---Sampling frequency above that is needed because 2x sampling frequency from Nyquist's theorem does not really work IRL because real low pass filters are not perfect and thus you want more margin. 44kHz sampling works good enough not because it works fine for 20kHz but because even though humans can hear high frequencies, they do it poorly. And neither actual sound contains much in that part of spectrum.
--- End quote ---

Before they used oversampling ADCs and DACs, 8th order elliptic filters sort of met the needed specifications, however anything modern uses oversampling ADCs and DACs and digital filtering so the antialiasing requirements are easily met now.  The aliasing filter problem does not apply to modern 44.1kHz equipment.


--- Quote from: gf on September 15, 2023, 11:56:47 pm ---:-+ And I also don't see why the relation tr = 0.35 / BW would apply here, which is rather the 10%...90% risetime of the step response of a Gaussian filter with a given -3dB bandwidth. This waveform is not a sine wave, but the integral of a Gaussian bell.
--- End quote ---

It still mostly applies, just like the 0.35 rule works for oscilloscopes with their bandwidth filter engaged which is decidedly not a Gaussian response.  I tested this once with a Tektronix 7A22 set at various bandwidths and 0.35 matched exactly, as I suppose Tektronix intended it to.

The fastest slew rate will be from a combination of frequencies so a step response, which has a comb of high frequencies, into the bandwidth filter will give a good approximation of the highest slew rate.

gf:

--- Quote from: David Hess on September 17, 2023, 01:13:28 pm ---
--- Quote from: gf on September 15, 2023, 11:56:47 pm ---:-+ And I also don't see why the relation tr = 0.35 / BW would apply here, which is rather the 10%...90% risetime of the step response of a Gaussian filter with a given -3dB bandwidth. This waveform is not a sine wave, but the integral of a Gaussian bell.
--- End quote ---

It still mostly applies, just like the 0.35 rule works for oscilloscopes with their bandwidth filter engaged which is decidedly not a Gaussian response.  I tested this once with a Tektronix 7A22 set at various bandwidths and 0.35 matched exactly, as I suppose Tektronix intended it to.

The fastest slew rate will be from a combination of frequencies so a step response, which has a comb of high frequencies, into the bandwidth filter will give a good approximation of the highest slew rate.

--- End quote ---

Yes, 0.35 seems to be the tr*BW product of traditional Tek scopes. An ideal Gaussian step response has actually 0.332 (which is of course pretty close).
[ Edit: An ideal Gaussian filter is not realizable anyway. In the analog domain, approximations like "Gaussian to -6dB" seem to be common, and in the digital domain the infinite extent needs to be truncated/windowed, so that we end up with an approximation, too. ]

My point was that the calculation 1.6*Apeak/tr = 1.6*Apeak/(0.35/f) leads to 4.57*f*Apeak, which underestimates the maximum slew rate of a sine wave Apeak*sin(2*pi*f*t), whose maximum slew rate is actually 2*pi*f*Apeak = 6.28*f*Apeak.

gf:

--- Quote from: Nominal Animal on September 16, 2023, 06:05:51 pm ---Does the DAC have more stringent slew rate requirements?  Slewing from rail to rail in a single sample period is \$2 \, V_{pk}\$ in one 44100'ths of a second, or \$88200 \, V_{pk}\$ per second, which is less than the aforementioned reconstruction limit.  This means that with a theoretically perfect brick-wall low-pass filter, the \$0.1385 \, V_{pk}\$ slew rate suffices, but this slew rate is \$1.5707\$ times (\$\pi/2\$) as fast as just slewing from rail to rail in a single sample period.  This affects our choice of DACs, as just being able to slew from rail to rail in a single sample period is not sufficient; it needs to slew basically 1.5707 times rail-to-rail range, in a single sample period.

If we did a Fourier analysis of the error spectrum at different (higher than necessary) DAC slew rates, we'd find a faster slew rate does push the error noise somewhat higher in the output spectrum, which makes it easier to filter out this particular error using analog circuits.  Note that we're still assuming a brick-wall low-pass filter at 22050 Hz for reconstructing the highest-frequency components in the audio signal, though.

--- End quote ---

A DAC emits a pulse with a particular shape for each sample. In order to avoid non-linear distortion, the pulse shape must be the same for each sample (except for differently scaled amplitude, of course).

However, the only pulse shape which enables "perfect reconstruction" is a Dirac delta pulse, i.e. in order to obtain an ideal, undistorted reconstruction (after applying the brickwall filter), the DAC would need to output a Dirac delta pulse for each sample (which requires infinite slew rate, of course).

For any other pulse shape, the output of the DAC can be considered as if it were the above mentioned stream of delta pulses, convolved (in the continuous-time domain) with the DAC's pulse shape. The consequence is that any pulse shape other than Dirac delta leads to linear distortion, or in other words, it affects the frequency response. The convolution with the pulse shape acts as a filter.

The linear interpolation between the samples you are considering above corresponds to a (hypothetical) DAC which emits a triangular pulse with FWHM=1/fs for each sample. This results in a sinc²-shaped lowpass frequency response, whose roll-off approaches 20*log10((sin(pi/2)/(pi/2))^2) = -7.84dB at fs/2 (or for for CD audio at 44.1kSa/s, it would be about  -6.3dB at 20kHz).

If you want to compensate this frequency roll-off in the digital domain before sending the data to the DAC, then you need additional dynamic range headroom for up to 2.47x higher amplitudes being sent to the DAC (implying the need for a 2.47x higher slew rate for the triangular pulses as well).

BTW, I guess that many are not aware that even the commonly used rectangular pulse shape with a pulse width of 1/fs (a.k.a. first-order hold) introduces a sinc-shaped frequency response roll-off (in the amount of e.g. -3.1dB at 20kHz, for CD audio at 44.1kSa/s).

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