Why does a DDS need a reconstruction filter?

Q: Why does a DDS need a reconstruction filter?

Q: Why does a DDS need a reconstruction filter? A: ADI’s DDSs include an integrated DAC, which converts the “numerical” sinusoid produced by the DDS to an analog sinusoid waveform like that in Figure 1. Figure 1 This picture is an example of the DAC output signal when the DDS is generating a relatively high output frequency (approximately 1/18 th of the sample DAC sample rate). This clearly illustrates the sampled nature of the DAC output. The sampled nature of the DAC output as shown in Figure 1 is the primary reason for the need of a reconstruction filter. The time domain signal in Figure 1 appears in the frequency domain like Figure 2. Figure 2 In Figure 2, fc is the sampling frequency (i.e., the DDS clock frequency). The vertical black line at approximately 0.1fc represents the magnitude of the output frequency of the DDS. The vertical red lines represent the images of the fundamental, which are a consequence of sampled DDS output. Notice that there is a roll off at the frequency response of the signal before 0.5fc and the images are located beyond 0.5fc. So the role of the reconstruction filter is to significantly attenuate the images while preserving the fundamental. The result is near perfect “reconstruction” of the sinusoid signal. This FAQ was generated from the following discussion: Why does a DDS need a reconstruction filter?

Question

Accepted Answer

Q: Why does a DDS need a reconstruction filter? 
 A: ADI&rsquo;s DDSs include an integrated DAC, which converts the &ldquo;numerical&rdquo; sinusoid produced by the DDS to an analog sinusoid waveform like that in Figure 1. 
 
 Figure 1 
 This picture is an example of the DAC output signal when the DDS is generating a relatively high output frequency (approximately 1/18 th of the sample DAC sample rate). This clearly illustrates the sampled nature of the DAC output. The sampled nature of the DAC output as shown in Figure 1 is the primary reason for the need of a reconstruction filter. The time domain signal in Figure 1 appears in the frequency domain like Figure 2. 
 Figure 2 
 
 In Figure 2, fc is the sampling frequency (i.e., the DDS clock frequency). The vertical black line at approximately 0.1fc represents the magnitude of the output frequency of the DDS. The vertical red lines represent the images of the fundamental, which are a consequence of sampled DDS output. Notice that there is a roll off at the frequency response of the signal before 0.5fc and the images are located beyond 0.5fc. So the role of the reconstruction filter is to significantly attenuate the images while preserving the fundamental. The result is near perfect &ldquo;reconstruction&rdquo; of the sinusoid signal. 
 This FAQ was generated from the following discussion: Why does a DDS need a reconstruction filter?