Equation 17:

en = [An -An-1] tjn ts

This analysis is similar to Blesser's approach in examining slew limiting in DAC output stages.12 The frequency domain representation E100%(f) of this error sequence can be obtained by taking the discrete Fourier transform of en:

Equation 18:

E100% (f) =F(en)
= fs F([An - An-l] tjn)
= fsΣ n=0 N-1 [An - An-1] tjn e -i2 π fnt
s

where: F is the discrete Fourier operator;
N is the number of samples forming the discrete error sequence;
f can take on values of kfs/N where k is an integer;
i is the complex variable √(-1).
Equation 18 indicates that the error spectrum for the 100% model should involve intermodulation components at


12 B.A. Blesser, of Audio,"JAES, October 1978, Vol.26.

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(a)

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Fig.23 DAC jitter error models: a) 100% sample DAC (top); b) Impulsive sample DAC (bottom).

signal/jitter sum and difference frequencies; this can be confirmed by simulating a jitter error signal using the model.

Fig.24a shows the unjittered spectrum of a 16-bit-quantized, 0dBFS, 10,001Hz audio signal, where the choice of excitation frequency has led to a flat quantization noisefloor even though no dither has been used. Fig.24b shows the same signal, but now corrupted by a lkHz jitter signal of peak amplitude 10ns. As expected, the error components in the jittered spectrum occur as sidebands at 10kHz +- 1kHz at approximately -71dBFS.

The An - An-1 factor in Equation 18 makes the magnitude of the error spectrum roughly proportional to the frequency as well as the amplitude of (he audio signal. This is illustrated in the simulated error spectrum of fig.24c for a 0dBFS, 2001Hz sinusoid, again jittered at 1kHz; due to the fivefold drop in excitation frequency, the sidebands are now approximately 14dB lower than the 10kHz example.

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(a)
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Fig 24 Simulated jitter error spectra for 100% DAC model (from top to bottom): a) 10,001Hz at 0dBFS audio, no jitter; B) 120,001Hz at 0dBFS audio, 10ns peak, 1kHz jitter; c) 2001Hz at 0dBFS audio, 10ns peak, 1kHz jitter.


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