Here’s something I’d completely forgotten about, or perhaps never known. The ‘Scarlett Book’ for SACD recommended that the high resolution audio be low pass filtered at 50kHz (@-3dB). I was reminded/informed of this by the datasheet for the Cirrus Logic CS4398 DAC.
What then to make of this insert that appeared in just about all SACDs in the early days?
A lot rests on the word ‘theoretically’.
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So, here’s another signal generator to compare to those I looked at in ‘Noise and distortion in signal generation’. This is the Siglent SDG1020 , a dual output 20MHz, arbitrary waveform model. It uses 14 bits of resolution apparently.
Here’s its noise performance. Channel 2 output (Channel 1 is identical), 1kHz sine wave recorded using a Focusrite Forte ADC at 24 bits, 96kHz using the ASIO interface with Reaper to preserve full resolution, then examining the file in CoolEdit 2000. I neglected to record the output levels in the previous post. This one I had it set to 4 volts peak-to-peak:
A slight improvement over the Velleman, but not all that much.
What was a big improvement was the square wave rise time (as you’d expect, since the Velleman is only a 1Mhz unit). As a reminder, here’s the zoomed in leading edge of a 1V p-p sine wave with the Vellemen:
You can read the rise time off the info bar near the bottom: 233 nanoseconds.
And here’s the same from the Siglent:
A bit of overshoot there
, but a hugely fast rise time. The info bar shows 5 nanoseconds, but it was actually toggling between 5 and 9. Still, that’s pretty damned fast. That overshoot is present regardless of output frequency or level. I wonder if there’s a calibration adjustment.
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(I have written an article for Australian HI-FI suggesting that a good way to start to understand the differences between 16 and 24 bit audio is to listen to the differences between 8 bit and 16 bit audio. To that end I will in the future be posting I have posted four versions of a musical excerpt here. In the meantime, I want to explore a weirdness that my experiments revealed, and explain why it happened.)
Let’s create a sine wave of 980 hertz with a sampling rate of 44.1kHz and 16 bits of resolution. Let this sine wave be of an extremely low level, with a peak of -80dB. Here’s its spectrogram:
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(This was generated with a small amount of dither, which is why it has a noise floor at -138dB and is unaccompanied by the nasty harmonics that would normally be present with a sine wave that is sketched out in values of +3 to -3). Note that the spike reaches -80dB.
Now let’s downsample it to 8 bits, accompanied by some dither noise:
Note the very high level of the noise, to the point that the 980 hertz signal barely peeks out over the top. This signal’s spike reaches -80dB, just as it did before it was downconverted.
So let’s go back to the 16 bit original and downsample it again to 8 bits, this time with some aggressive noise shaping:
That’s better. The 980 hertz signal stands well out from the signal, and if you turn the whole thing up it is clearly audible. It, once again, reaches -80dB.
Now what I’ve been leading up to: again we return to the 16 bit original, and again we downsample to 8 bits. But this time there’s no dither, no added low level noise. Instead we simply divide the 16 bit value of each sample by 8, and map it onto the nearest 8 bit integer value. Here’s the spectrum:
Lots of harmonics, quite a bit of noise (although a lower level than with the plain dithering) and something that’s distinctly odd. Instead of the 980 hertz spike reaching -80dB, it makes it up to -48dB. How could reducing its precision from 16 bits to 8 bits have caused that?
Well, here’s the thing: -80dB is lower than minimum value definable in an 8 bit signal. The lowest quantisation level is -48dB. So the only way this wave form can be represented is by toggling between values for zero and one. Let’s zoom in on the wave form:
As you can see
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, our sine wave has become a kind of square wave, which explains all those harmonics. But it also explains why the fundamental is way too powerful. A sample value of ‘1’ is -48dB on an 8 bit scale, so that’s what our signal becomes.
Which is why dither is so vitally important
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, at least with 8 bit audio.
Here are the four test signals with the low level 980 hertz sine wave:
Download them and listen. You’ll have to turn up the volume quite a way to hear the 980 hertz tone.
And here are the four excerpts of the music from the group B’Jezus referred to in the article:
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