The lower portion of this slide is a block diagram showing how the DAC and digital inverse sinc filter are interconnected. The DAC and digital filter both share the same sample clock, namely the system clock. In the context of a DDS, the D-bit bus on the far left comes from the output of the map (i.e., the angle-to-amplitude converter). A multiplexer separates the input of the DAC from the output of the digital filter which allows for selecting or bypassing the inverse sinc filter under program control. The plot demonstrates the function of the inverse sinc filter as follows. The blue trace is the magnitude of the sinc response, that is, the frequency dependent roll off of the DAC output signal due to its zero-order hold function. At the Nyquist frequency (one half Fs) the sinc response is down 3.92dB relative to its magnitude at DC, as shown by the intersecting dashed lines. The blue trace is effectively the shape of the DAC output spectrum with the inverse sinc filter bypassed. The red trace is the frequency response of the digital inverse sinc filter (as determined by its digital tap coefficients). Note the filter response has 3.92dB of loss at DC. This constitutes the insertion loss of the filter. The filter applies progressively less loss to higher frequencies up to the Nyquist frequency. The shape of the filter response is an exact inverse of the shape of the sinc response. The green trace shows the combined response of the inverse sinc filter and DAC output. Because the filter response is exactly inverse to the sinc response, the combined response is essentially flat from DC to the Nyquist frequency. However, from the Nyquist frequency up to the sampling frequency (Fs), which constitutes the second Nyquist zone, the filter response changes to the gray trace. The gray trace is essentially a mirror image of the filter response in the first Nyquist zone, which has a significant impact on the combined response as shown by the green trace in the second Nyquist zone. As one can see, the presence of the inverse sinc filter causes the DAC output spectrum to roll off in the second Nyquist zone even steeper than it would without the filter (the blue trace). Hence, if one elects to use the DAC output signal in any Nyquist zone other than the first, the inverse sinc filter should be bypassed.