X-Stream Operator’s Manual
WM-OM-E Rev I 219
excellent step response in 0.5 bit steps, and minimum bandwidth reduction for resolution
improvements of between 0.5 and 3 bits. Each step corresponds to a bandwidth reduction factor of
two, allowing easy control of the bandwidth resolution trade-off. The parameters of the six filters are
given in the following table.
Resolution
increased by
-3 dB Bandwidth
(× Nyquist)
Filter Length
(Samples)
0.5 0.5 2
1.0 0.241 5
1.5 0.121 10
2.0 0.058 24
2.5 0.029 51
3.0 0.016 117
With low-pass filters, the actual SNR increase obtained in any particular situation depends on the
power spectral density of the noise on the signal.
The improvement in SNR corresponds to the improvement in resolution if the noise in the signal is
white -- evenly distributed across the frequency spectrum.
If the noise power is biased towards high frequencies, the SNR improvement will be better than the
resolution improvement.
The opposite may be true if the noise is mostly at lower frequencies. SNR improvement due to the
removal of coherent noise signals -- feed-through of clock signals, for example -- is determined by
the fall of the dominant frequency components of the signal in the passband. This is easily
ascertained using spectral analysis. The filters have a precisely constant zero-phase response.
This has two benefits. First, the filters do not distort the relative position of different events in the
waveform, even if the events' frequency content is different. Second, because the waveforms are
stored, the delay normally associated with filtering (between the input and output waveforms) can
be exactly compensated during the computation of the filtered waveform.
The filters have been given exact unity gain at low frequency. Enhanced resolution should therefore
not cause overflow if the source data is not overflowed. If part of the source trace were to overflow,
filtering would be allowed, but the results in the vicinity of the overflowed data -- the filter impulse
response length -- would be incorrect. This is because in some circumstances an overflow may be
a spike of only one or two samples, and the energy in this spike may not be enough to significantly
affect the results. It would then be undesirable to disallow the whole trace.
The following examples illustrate how you might use the instrument's enhanced resolution function.
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