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In the previous lesson, users were shown how a sampled DAC’s inherent zero-order hold effect results in a distorted output spectrum. The distortion is frequency dependent and follows a magnitude response according to the sine-x-over-x, or sinc function, as defined here. Because the sinc response is deterministic, it is possible to design a filter to compensate for its effect over a limited bandwidth. In fact, because a high speed DDS typically relies on a sampled DAC, it is possible to take advantage of the sampling process and use a digital filter to compensate for the sinc roll off. This is done by placing a digital filter at the input to the DAC and having the filter sample at the DAC sample rate. The digital filter effectively pre-processes the data fed to the DAC in the time domain. With the proper digital filter coefficients, the frequency response of the digital filter can be made to follow an inverted form of the sinc response. With the input data to the DAC adjusted by the digital filter to follow an inverted sinc response, the sinc response imposed by the DAC should be effectively cancelled. The net result is a flat frequency response in the DAC output spectrum.
