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Why does a DDS need a reconstruction filter?

DDS evaluation boards always a filter at the output. Why?

  • A DDS is known as a Nyquist device. That is, it relies on a sampling clock (the system clock) to produce the output signal. A consequence of sampling is that the output spectrum is periodic in multiples of 50% of the sampling clock frequency. For example, let's assign Fs as the sampling clock frequency. Then, any frequency produced by the DDS resides in the region between DC and 1/2*Fs (the 1st Nyquist zone). Sampling, however, causes replicas of the spectrum in the 1st Nyquist zone to be repeated (indefinitely) in the odd Nyquist zones: Fs to 3/2*Fs, 2*Fs to 5/2*Fs, etc. It addition, mirror image replicas of the spectrum in the 1st Nyquist zone repeat (indefinitely) in the even Nyquist zones: 1/2*Fs to Fs, 3/2*Fs to 2*Fs, etc.

    The spectra in the Nyquist zones other than the first are called Nyquist images. The purpose of the filter at the output of the DDS is to suppress the Nyqist images but retain the spectrum in the 1st Nyquist zone. This filter is called a reconstruction filter (because in takes the sampled DDS output and attempts to reconstruct the original time domain waveform). For example, without the filter the DDS output looks like a sine wave with a staircase superimposed (the effect of sampling). The filter removes the staircase and restores the original sine wave; i.e., it reconstructs the original sine wave from the sampled sine wave.

    The role of a reconstruction filter is synonymous with the role of an antialias filter. The difference being that an antialias filter band limits an analog signal so that it can be properly sampled, whereas a reconstruction filter band limits a signal that has been digitally sampled in order to restore it to its original analog form.

    NOTE: If a particular application is not adversely affected by the presence of spectral content beyond the 1st Nyquist zone caused by sampling, then a reconstruction filter is not necessary.

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