As explained earlier, a digital waveform must be updated at least twice as fast as the highest frequency of the desired analog signal to be accurately generated. Even though the theoretical requirement for sample clock, fs, is twice that of the signal bandwidth, f0, images are introduced in the output signal at |f0 ± nfs|, as shown in the Figure 11. The images degrade the spectral purity of the signal, creating the need to filter these images out of the signal.
To create quality signals, most signal generators have the ability to lowpass filter the signal being generated. A lowpass filter is used to smooth the raw DAC output. The filter removes high-frequency aliased components that are introduced through the digital generation of the signal. You can implement the lowpass filter through both analog and digital filters.
Designing an analog filter that rejects the images and yet gets maximum output bandwidth (0 to 0.43fs) is difficult and near impossible, and is represented in Figure 6 by the curve, Analog Filter 1. Analog Filter 2 represents a more practical filter. This filter is not as aggressive as Analog Filter 1. Analog Filter 2 does not filter out the images near fs, but it does reject all the others. Analog filters have trade-offs between the roll-off of the attenuation after the 3 dB point and the flatness of the attenuation before the 3 dB point.
The third filter, Analog Filter 3, has a much higher 3 dB point than the first two analog filters. Because of the higher 3 dB point, the filter is very nearly flat in the passband (0 to 0.43fs). Analog Filter 3 does not filter the images produced at fs and 2fs at all, but this shortcoming can be alleviated with a digital interpolation filter.
To ease the requirements of the analog filter and to get more output bandwidth, signal generators often use digital filters to interpolate data between the stored waveform data. For example, in a 2x interpolation, the DAC would interpolate 1 point between each digital sample. Most NI Signal Generators offer 2x, 4x, and 8x interpolation options. To generate the most spectrally pure signals using the digital filter, you should use the highest interpolation factor that you can.
In Figure 13, the two times interpolating filter is used and the effective sample rate of the DAC is 2fs. The images at fs ± f0 are no longer an issue, and the images are now at |2fs ± f0|.
Now, Analog Filter 2 can easily filter out all the images due to the digital generation of the signal. This behavior is seen in the frequency domain representation and in the time domain.