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W
R
X
S
AVE
UNNER
I
ERIES
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 pass band. 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 give
n 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.
132
WRXi-OM-E Rev C
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