The output of a Digital to Analog converter has a magnitude roll-off in frequency as a Sinc function with the first null at the sampling rate. Why is this the case?
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2$\begingroup$ look up Zero-order hold. $\endgroup$– robert bristow-johnsonCommented Jun 23, 2017 at 16:59
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Not ALL DACs (D/A converter) do this, but a traditional DAC operates on the digital samples as a zero-order hold; each sample is held in the analog at a constant value until the next sample. This process is identical mathematically to convolving the discrete samples (as weighted impulses) with a rectangular function of width T where T is the sample time.
The Fourier Transform of a rectangular function of width T is a Sinc function with first null at 1/T, where 1/T is the sampling rate.
Convolving in the time domain is equivalent to multiplying in the frequency domain, so the spectrum of your discrete signal is multiplied by the Sinc function in the process of analog reconstruction in the DAC due to the zero order hold.
There are other DAC implementations that reduce this effect such as interpolating DACs and "Return to Zero" (R2Z) DACs. An R2Z DAC forces the output to return to zero prior to the next sample, reducing T and therefore pushing out in frequency where the first null occurs (therefore reducing passband rolloff).
