The subsequent images show some examples of DDS based wave generation.

Example 1

At a sampling frequency of 44.1 kHz, as used in standard audio recordings, heavy filtering is required to generate a high-frequency sine wave with few harmonics. If as shown here  a double-T filter is used, which has an attenuation ratio of 1:50 (0.02 <-> 0.98) in the digital domain, a suitable waveform can already be generated that might be adequate for simple audio applications. The optical deviations are caused by higher harmonics that are barely audible. However, the analog wave exhibits a certain amount of drift in the low-frequency range, which is caused by beat frequencies. The steep filter also causes a significant phase shift. For more demanding applications, however, this is not sufficient. In such cases, a cascaded Linkwitz filter, for example, is required.

The image shows the case for a 20kHz audio frequency. The amplitude is already reduced down to less than 50% because of the used edge frequency of the filter.

Example 2

With 15kHz, strong deviation and phase offset, as well as low frequent drift can be observed. A simple filter is not enough.

Example 3

The same frequency (15kHz) generated with a sampling frequency of 96kHz shows less unwanted issues. This is even appropriate for industrial applications.

Example 4

For audio only the filter can now be modified in that way, that less deviation and phase offset occurs. Here a 0,05 <->0,95 ratio of the filter (digital representation) is used.

Example 5

Even the 20kHz wave is pretty fine for audio now! This low distortion may be accepted for audio well. 

Example 6

Using 192kHz of sampling frequency, the filter's edge frequency could be further increased. Here a 0,2 <-> 0,8 ratio is used. 20kHz is nearly perfect now and has only a low number of harmonics left. 

Example 7

Even 25kHz is fine. A comparison to a real sine wave shows less than 4% THD over the full spectrum using a double cascaded filter. 

Read the old article and some issues with DDS