is also of interest that a typical analog transfer function non-linearity will result in PID where the timing error ia highly correlated with the audio signal. This observation lends weight to the analogy made between P ID and digital audio interface jitter, where we have shown that the jitter resulting from a band-limited digital interface can also strongly correlate with the transmitted audio signal. Of course, PID in analog amplifiers is intimately linked with closed-loop amplitude non-linearity, and is not in itself a cause of additional error, while jitter in digital audio interfaces is a source of error in A/D or D/A conversion.

Nevertheless, the analogy between PID timing error and interface jitter is useful if the overall timing error in a system is to be minimized; there is little point in minimizing digital audio interface jitter if the analog circuitry preceding or following conversion is of poor quality. In general, it is rewarding to make comparisons between analog and digital system artifacts, an exercise that has shown interesting results before. 21 22 In truth, the boundaries between analog and digital systems are not as clear-cut as they may at first appear, and we encourage system appraisal in a global sense.

AUDIBILITY OF JITTER ERRORS
How much jitter is tolerable in a reconstructed stereo PCM transmission? One of the earliest studies of the audible consequences of jitter is due to Manson, 23 who carried out a


21 M.J. Hawksford, "Fuzzy Distortion in Analog Amplifiers: A Limit to Information Transmission?,"JAES, October 1983, Vol.31, pp.745-754.
22 MJ. Hawksford, "Nth.-Order Recursive Sigma-ADC Machinery at the Analogue-Digital Gateway," presented at the 78th AES Convention, May 1985, Preprint 2248.

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Fig.31 Simulated jitter error spectra for 100.01Hz at 0dBFS, 10nS peak, 4kHz jitter, for a) 100% DAC model (top) and b) impulsive model (bottom).

series of tests using a monophonic analog sign input to a sampling device with a stable dock. sampled (but unquantized) audio signal is then converted back tO the analog domain Using a sample-and-hold unit with a controlled amount of clock jitter, and auditioned. Manson suggests that 35ns RMS jitter represents the threshold of subjective impairment using critical source material. However, we believe that several factors make this an unrealistically high figure of "minimum audible jitter."

First, Manson's experiments were carried out using a monophonic test signal. Much evidence suggests that audibility of low-level distortion (as would be caused by jitter) increases when music is reproduced in stereo, as' acoustic objects are now perceived in two-dimensional space, and masking of errors by the primary signal is not so effective. Second, these tests were carried out some time ago, using tape recordings; the advances in reproduction equipment now available to the consumer should result in a lower threshold.

A better estimate of the audible jitter threshold can be obtained by examining the jitter error sequence, and assuming that it will be inaudible if below the level of quantization noise present in the system for any possible excitation frequency. Lidbetter24 thus arrives at a value of 120 picoseconds for a 16-bit, 100% sample DAC, and an incredibly low 8ps for a 20-bit system. Shelton,25 Fourre,26 Harris,27 van Wil-


23 C Manson, "Digital Sound Signals: Subjective Effect of Timing Jitter," BBC Research Department Engineering Report 1974/11 (March 1974).
24 P.S. Lidbetter, "Basic Concepts and Problems of Synchronization of Digital Audio Systems," presented at the 84th AES Convention, Match 1988, Preprint 2605.

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Fig.32 Measured jitter error spectra for 100.01Hz at 0dBFS, 10ns peak, 4kHz jitter, for a) Musical Fidelity Digilog (top) and b) Meridian 203 (bottom).


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