I/Q signal generation applications place high demands on signal generator spectral purity. To minimize distortion from the digital-to-analog reconstruction images, NI 5421 generators use a combination of digital and analog filtering designed to optimize passband flatness, phase linearity, and image suppression.
You must update the DAC samples at least twice as fast as the bandwidth of the analog signal you wish to accurately generate. Even though the theoretical requirement for sample clock (fs) is twice that of the signal bandwidth (fo), images are introduced in the output signal at |fo ± nfs|, as shown in Figure 5. These images, which degrade the signal spectral purity, must be removed with a lowpass filter.
Figure 5. Digital-to-analog signal reconstruction creates undesired sampling images.
To understand data interpolation and its effects on spectral purity, suppose there are three different analog filters with varying cutoff frequencies and orders. The three filters are represented in Figure 6 along with the sampling images. The ideal analog filter is represented as "analog filter 1." Because this filter attenuation is very steep, it is also very expensive to implement, and requires a large amount of board space. Additionally, it cannot achieve the passband flatness required for I/Q applications. Analog filter 2 represents a more practical filter; however, it will not attenuate the images near fs. Because analog filters have trade-offs between the attenuation steepness after the cutoff frequency and the flatness before the cutoff frequency, selecting the ideal filter values heavily depends on the DAC sampling rate and the waveform frequencies generated. It is impossible to design a single analog filter that accommodates flexible sample rates and output signal frequencies while maintaining strict performance requirements.
Another critical analog filter specification is group delay - the amount of time needed for a signal having finite time duration (such as a pulse) to pass through the analog filter. In an ideal filter with linear group delay, all frequencies present in the signal have the same time delay, so that the output signal is not phase-distorted.
The third filter, analog filter 3, has a much higher cutoff frequency than the first two analog filters. Because of the higher cutoff frequency, the filter is very nearly flat in the passband (0 to 0.43fs). The images produced at fs and 2fs fall within the passband of filter 3, so they are not attenuated at all, but this shortcoming can be alleviated with a digital interpolation filter.
Figure 6. Sampling images must be filtered to improve spectral quality, but different filter implementations must be considered.
To simplify the analog filter requirements and achieve good specifications for a range of sampling rates and output frequencies, the NI 5421 devices use a half-band finite impulse response digital filter to interpolate one, three, or seven samples between every two waveform samples at two times, four times, and eight times the sampling frequency (fs). The DAC then internally operates at an effective sampling rate that is two times (2fs), four times (4fs), or eight times (8fs) the sampling frequency - specifically, the rate at which the data is clocked from the memory into the DAC.
In Figure 7, using a two times-interpolating filter increases the DAC effective sampling rate to 2fs. The first set of reconstruction images is now located at |2fs ± fo|, which falls in the filter 2 stop band.
Figure 7. Interpolation increases the sampling rate, causing the images to shift to higher frequencies.
Now, analog filter 2 can easily filter out all the images caused by the digital signal generation, as seen in the frequency-domain representation in Figure 7, and in the time-domain representation in Figure 8.
Figure 8. In the time domain, interpolation has the effect of smoothing otherwise sharp sample transitions.
Using 2x interpolation filtering and increasing the DAC effective sampling rate to 2fs better eliminates images, and generates a signal with better spectral purity. However, increasing the interpolation filter to 4x further improves the output signal.
Figure 9 shows a signal image with 4x interpolation and a DAC effective sampling rate of 4fs. The images are shifted up to 4fs, where they are well above the filter 3 cutoff frequency. This configuration, used in the NI 5421, eliminates the spectral images and has a maximally flat filter within the passband. The configuration approaches an ideal design in digitally generating spectrally pure waveforms. An NI 5421 achieves ±0.25 dB passband flatness to 40 MHz and a total harmonic distortion of -75 dB at 1 MHz.
Figure 9. The combination of digital interpolation and analog filter results in the best flatness and image rejection.