Who wants to do an experiment? Suppose we have two signals, both consisting of a 1 kHz sine wave, the only difference being that one is shifted in time. The difference between these signals will then also be a 1 kHz sine save with phase and magnitude dependent on the amount of time shift. With a time difference of 300 ps, the difference signal is a pure tone at about -114 dB:
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If we round both signals to 16-bit precision (without dither) before calculating the difference, we get a very different result:
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The difference is barely large enough to change the LSB of a few samples. The difference spectrum has components every 100 Hz, all around the same level. With this level of precision, all we can say is that something changed.
Adding TPDF dither before rounding to 16 bits gives a very different result:
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Although, the waveform still bears little resemblance to a sine wave, the spectrum now shows a single spike of the correct frequency and amplitude. Compared to the reference, the only difference is the addition of uniform noise. It should be noted, however, that this spectrum was averaged over several seconds.
With a 10 kHz signal, keeping the 300 ps time shift, the difference is 10x larger in amplitude:
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With rounding to 16 bits, the difference spectrum is still ugly, though now the 10 kHz component stands out from the rest at roughly the correct amplitude:
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Once again, adding TPDF dither before rounding fixes things:
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I'm not sure if this actually answers any of the questions posed above.
... The noise shaping gives you better timing resolution due to improved SNR at low frequencies at the loss of SNR at high frequencies.
