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I saw a graph like the one in the picture and frankly I could not fully understand the difference between quantization artifact and spur. (ref. The Data Conversion Handbook Walt Kester (Editor) page 87)

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What are the differences in the spectrum between these two concepts? How can I distinguish the two when I look at the spectrum?

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  • $\begingroup$ As the handbook states: "Note that this variation in the apparent harmonic distortion of the ADC is an artifact of the sampling process and the correlation of the quantization error with the input frequency." Meaning the harmonics (spurs) can occur due to the quantization and due to the sampling process. So is it right to assume that you are asking for the difference of harmonics due to the sampling process and harmonics due to quantization? $\endgroup$
    – Irreducible
    Commented Jul 8 at 11:28

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The difference here is that the first signal has an integer number of periods in the DFT window and the second one doesn't. That means for purposes of the DFT, the first signal is periodic and the second one isn't.

Periodic signals have periodic quantization noise. Hence the noise spectrum has spurs: the noise only occurs at multiples of the signal frequency.

For non-periodic signals, the quantization tends to be uniformly distributed and the quantization noise is white, i.e. about equal energy at all frequencies. There are exceptions to this, but we'll ignore this for now.

Note that the right signal has no spurs but the average noise level is higher. The total quantization noise for both signals is roughly the same, they are just differently distributed in frequency.

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  • $\begingroup$ Hil, here is spot on. If the sinusoidal input is periodic and perfectly in-sync with the FFT frame and has period that is an exact integer multiple of the sampling period, the input voltage will repeat exactly ever period, and so the quantization error will repeat exactly every period and your error signal is a noisy-looking but very periodic signal. Note that there are only odd harmonics. That means that the quantization error is symmetrical for the negative half-sine as to the positive half-sine. Curious that there is 15th harmonic, but no 13th harmonic. Dunno why. $\endgroup$
    – robert bristow-johnson
    Commented Jul 8 at 15:43
  • $\begingroup$ @Hilmar Really great explanation. Thank you. I understand this. Periodic sampling introduces quantization artifacts but does not increase the noise floor. When it is not periodic, the noise floor increases but no artifact occurs. So, based on what should I determine the number N? It seems like taking it periodically is always inconvenient. On the other hand, isn't there a difference between quantization artifacts and spurs? Are quantization artifacts actually a spur? $\endgroup$
    – bb0667
    Commented Jul 9 at 14:01
  • $\begingroup$ @robertbristow-johnson I didn't pay attention to harmonics. But yes, harmonics in odd coefficients actually appeared. What is the reason for it appearing in odd numbers? Why did the even coeff. disappear? $\endgroup$
    – bb0667
    Commented Jul 9 at 14:04
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    $\begingroup$ It's called half-wave symmetry. It's a thing regarding Fourier Series. $\endgroup$
    – robert bristow-johnson
    Commented Jul 9 at 15:00
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    $\begingroup$ @bb0667: "On the other hand, isn't there a difference between quantization artifacts and spurs? " . Quantization generates noise. This noise can take different shapes, often it's uniformly distributed white noise, but it can also take other shapes like the harmonic noise in your example. "Spur" is generally a term used for peaks in the noise spectrum, i.e. single frequency or very narrow band noise. Spurs can be caused by quantization or by something completely different. Turning this around: quantization can result in spurs, a constant noise floor or something completely different. $\endgroup$
    – Hilmar
    Commented Jul 10 at 15:11

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