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When I sample a sine wave output of a DDS based bench function generator I have noticed there is always harmonics of the fundamental frequency. For example, below is the function generator's output set for 2Hz 1Vrms sine wave in time series and this is sampled by a 16-bit single ended DAQ at 1kHz sampling rate:

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And here is the FFT spectrum of the above stored signal.

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Then I went to a DDS chip's datasheet and observed this type of harmonics in some of the plots. I'm not sure whether these two are related but here below from page 9, one of such spectrum:

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What could be said about these observations about the harmonics? Is that because DAC part of the DDS? Or can that be a totally unrelated cause?

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    \$\begingroup\$ I guess it is due to aliasing. Quite common phenomena that you have to filter with analog filter, not possible if you want to have an arbitrary output frequency - large bandwidth. \$\endgroup\$ Commented Nov 15, 2018 at 11:01
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    \$\begingroup\$ @MarkoBuršičma. It almost exactly matches dstasheet spec. No reason to attribute this to aliasing \$\endgroup\$ Commented Nov 15, 2018 at 12:07

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What could be said about these observations about the harmonics?

Let's get this into perspective; the 2 Hz fundamental has an amplitude that is about 60 dB greater than the 2nd harmonic at 4 Hz. In real numbers 60 dB is a ratio of 1000:1 or 0.1%. This is not really that significant and given that the output of a DAC has an integral non-linearity error that can be several LSb it doesn't surprise me at all.

Above 6 Hz the spectrum is getting muddier but you are down in the real basement of the signal and DDS will produce artefacts at this very small level.

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Most DDS chips use a small ROM as a sine lookup table in order to generate the data that feeds the output DAC. This ROM has limited resolution in both time and voltage.

The fact that the ROM addresses generated by the DDS logic don't step symmetrically through the ROM (except at certain "special" frequency settings) means that there will be some low-level harmonic distortion in the output.

If you want to reduce this, you can add some extra band-pass or low-pass filtering in the analog domain.

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