Keysight M8194A - 7 Appendix Resampling Algorithms for Waveform Import; Resampling Requirements; Resampling Methodology

164 Keysight M8194A 120 GSa/s Arbitrary Waveform Generator User Guide
7 Appendix
Resampling Algorithms for Waveform Import
Resampling Requirements
Resampling is typically associated to a series of processes applied to a
waveform sampled at a given sampling frequency to generate a new
waveform with a different sampling rate while preserving all the original
information contained in the signal within the Nyquist bandwidth
corresponding to the output sampling rate. Processes involved in
resampling may vary depending on the output to input sampling rate ratio
(or resampling factor) and the integer nature of the ratio itself. Resampling
calculations, when applied to arbitrary waveform generation, must meet
additional constraints such as available record length boundaries, record
length granularity requirements, or acceptable sampling rate range.
Typically, the characteristics of the input waveform (sampling rate, record
length) are externally defined (i.e. by the horizontal settings of an
oscilloscope used to capture the waveform). Users may be interested in
resampling the signal to adapt the input waveform to the AWG
requirements or the user desires. In some cases, it may be necessary to
reduce the sampling rate if it has been captured at a higher sampling rate
than the one allowed by the AWG or to reduce the record length required
to generate it. The opposite is also true as oversampling may help to
“smooth” the signal as increasing sampling rate will shift the images
created by the DAC to a higher frequency. Finally, resampling may be also
necessary to adapt the record length of the input waveform to a legal
record length that can be applied to a real AWG (i.e. to meet the record
length granularities) without applying truncation or “zero padding” to the
input waveform.
Resampling Methodology
Generally speaking, resampling factors do not have to be an integer or a
simple fractional ratio. Because of that, traditional methods based in
upsampling/filtering/decimation techniques may not be suitable given the
amount of calculations resulting from the typical input waveform sizes
involved. Instead of this, a more straight forward approach has been
chosen. This approach is based in the following principles:
• Only output samples will be calculated so there is not any up-sampling
and/or down-sampling operations involved.
• Filtering calculations will be kept to a minimum by using a filter with a
fast enough roll-off and sufficient stop band attenuation according to
the target AWG dynamic range.