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Upsamplers, DACs, jitter, shakes and analogue withdrawals, this is it.

An attempt to answer multiple posts below

There seems to be a general lack of clarity as to the definition of terms that actually have precise technical meanings. I will attempt to clear these up in a straight forward way:

1) Jitter refers to the timing variations in what should be a *perfectly* steady reference timing signal. While all of us can understand the basic concept, it turns out that specifying the jitter level of a device, signal, clock, or whatever is not as useful as one would hope.

For starters jitter specifications are given in units of time (eg, picoseconds). This in itself can be misleading as the absolute amount of jitter (for example, 1 picosecond) can either be a very small percentage of a low-frequency clock (for example, 0.0000000001% of a 1 Hz clock) or a much higher percentage of high frequency clock (for example, 1% of a 10GHz clock.

A second problem is whether the jitter is specified as a peak value or an RMS value. Unfortunately there is no fixed relationship between these two as it depends on the source of the timing variations. For example if the jitter were due solely to power supply ripple affecting the jitter of a ciruit, the peak jitter would be 1.414x the RMS jitter. At the other extreme if random noise effects in the circuit are the source of the jitter, the peak jitter levels will *on-average* be 12x the RMS jitter levels. But as noise is a random event, there will be random times that the peak jitter will be greater that 12x the RMS value and other random times that the peak jitter will be less than 12x the RMS value.

A third problem with jitter is that it tells us nothing of the spectral distribution of the timing errors. Comparing with analog speed (timing) variations, variations is speed below about 5Hz creates a characteristic change in the sound that we describe as "wow". Faster speed variations from 5Hz to 20Hz give a different audible effect and we describe that as "flutter". Even higher speed variations (typically found in analog tape) are called "scrape flutter" and have yet another audible characteristic. Turning back to digital it is also known that the same levels of jitter concentrated at different frequency ranges will also have different audible consequences, but a hitter specification only gives us a single number, with no information as the the spectral distribution of those timing variations.

A fourth problem with jitter is that it does not tell us whether the jitter is correlated with the data or not. For example if one were to look at the spectral distribution when playing back a full-scale tones of various frequencies, if the spectral distribution of the jitter also changed it would be referred to as "correlated" jitter. If the jitter spectrum did not change, it would likely be due to random noise in the clocking circuits and would be referred to as "uncorrelated" jitter.

2) A much more useful way of describing timing errors in a digital system is to use a phase-noise plot (or graph). This shows the jitter levels at various frequency offsets from the main (carrier) frequency of an oscillator, and is typically used to characterize oscillators and (less commonly) phase-lock-loops. (NB: In the latter case the phase-noise plot of a PLL shows the amount of phase noise of the total system of a clock generator - typically some type of oscillator - and the PLL as a combined system.)

Unfortunately at this point in time even phase-noise plots have limitations. Only recently has sufficiently sensitive test equipment been designed to measure phase noise with accuracy, and these complex instruments are too expensive (between $15,000 and $100,000) and complex to operate to be widely used. There is not enough data to provide generally accepted correlations between the spectral distribution of jitter and its audible effects. Nor are oscillator circuits ever measured for phase noise when using anything but the very best laboratory power supplies - which may not reflect the performance of that same oscillator when used in an actual piece of digital audio equipment.

Another advantage of using a phase-noise plot is that by simply integrating the total amount of phase noise over a specified frequency range, one can calculate the amount of jitter that represents. However, the reverse is not true - one cannot determine the spectral distribution of a phase-noise plot from a jitter specification. This is similar to knowing the THD of an analog circuit compared to looking at an FFT of the analog waveform. The FFT will show how much of the distortion is 2nd harmonic, 3rd harmonic, and so on, and it is known that the ear is more sensitive to high-order harmonic distortions than low order ones. There is simply more information in the FFT plot compared to a single THD number.

3) It should be noted that these concepts are apparently too abstract or difficult for all to understand fully. For example in the linked video a digital designer made at least one inaccurate statement regarding jitter. Specifically that jitter generated by imperfect clocks in the A/D converter and embedded in the digital file could be attenuated (or even eliminated?) by using a low-pass digital filter that attenuates the high frequencies encoded in that file. I can't even begin to claim to understand what he was attempting to describe, except that it is not correct. The designer did note that he uses a master oscillator from Silicon Labs. These are interesting designs in that they do not use quartz crystals as their resonant element, but instead tiny strips of silicon etched into the semiconductor wafer itself (MEMS or Micro-ElectroMechanical Systems). This technology does not have the frequency stability required to reach low levels of phase noise at low frequency offsets from the oscillator (carrier) frequency. Again there is no consensus as to the audible effects of this, except to note that crystal-based oscillators have significantly better measured performance in this area.

As always, strictly my personal opinions and not necessarily those of my employer or you, the reader.

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