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Fig.33 Audibility of spectrally flat TPD 16-bit dither. Top curve is interpolated from the minimally audible field threshold data of ISO226, With 0dB equivalent to a sound-pressure level of 112dB at 1 m per loudspeaker.

lenswaard,28 and the recommendations embodied in AES11-199129 all quote similar values.

Are these lower limits reasonable? How audible is jitter


25 T. Shelton, "Synchronization of Digital Audio," Proceedings of the ALS 7th International Conference: Audio in Digital Times (Toronto, Ontario, Canada, 1989).
26 R.D. Fourth, "Testing 20-Bit Audio Digital-to-Analog Converters," Proceedings of the ALS 7th International Conference: Audio in Digital Times, (Toronto, Ontario, Canada, 1989).
27 Peter van Willenswaard, Stereophile, November 1988, Vol.11 No.11, pp.51-53.
28 S. Harris, "The Effects of Sampling Clock Jitter on Nyquist Sampling Analog- to-Digital Converters, and on Oversampling Delta-Sigma ADCs," JAES, July/August 1990, %138, pp.537-542.
29 AES11-1991, "ALS Recommended Practice for Digital Audio Engineering--. Synchronization of Digital Audio Equipment in Studio Operations,"JAES, March 199I, %139, pp.156-162.

when its level is at the quantization noisefloor? An attractive approach to answering these questions is to model the hearing process itself, ie, find out whether a given jitter error is below the masked threshold due to the jittered audio signal - a method adopted by Julian Dunn.30 Correspondingly, a simple hearing model was developed in order to assess the audibility of jitter in a band-limited interface.

Our model assumes that the error due to jitter is inaudible if it is below the threshold of hearing ('minimally audible field) at all frequencies. This approach will yield pessimistic results as far as error audibility is concerned, since the additional masking effect of signal tones is not considered, although masking of low-frequency noise by high-frequency tones is minimal. Recent work by Bob Stuart31 suggests that the audibility of errors in isolation may well be of higher significance than has previously been thought.

We define the threshold of hearing in the frequency domain by Passing a cubic spline through the threshold data of ISO22632 and scaling by the gain of a typical audio system under critical listening conditions such that "0dB" refers to a sound-pressure level of 112dB at 1m per speaker.33 The error signal is then integrated at each frequency bin across a bandwidth defined by the equivalent rectangular noise


30 J. Dunn, "Considerations for Interfacing Digital Audio Equipment to the Standards AES3, AES5 and AES11," Proceedings of the AES 10th International Conference: Images of Audio (London 1991).
31 J.R. Smart, Hi-Fi New &Record Review , January 1991, Letter to the Editor, p.15.
32 ISO226:1987, "Acoustics - Normal Equal-Loudness Level Contours for Pure Tones under Free-Field Listening 1987.
33 J.R. Stuart, 'Predicting the Audibility, Detectability, and Loudness of.Errors in Audio Systems," presented at the 91st AES Convention, New York, October 19 1991, Preprint 3209.

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Fig.34 Simulated jitter errors for RPD white jitter noise: a) 20kHz at 0dBFS, 180ps peak jitter, 100% DAC (top); b) 100Hz at 0dBFS, 55ps peak jitter, impulsive DAC (bottom).

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Fig.35 Simulated worst-case jitter errors for sinusoidal jitter: a) 22kHz at 0dBFS, 20ps peak jitter at 18.5kHz (top); b) impulsive DAC, 100Hz at 0dBFS, 75ps peak jitter at 4kHz (bottom).


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