User manual

WaveSurfer 3000/3000z Oscilloscopes Operator's Manual

The instrument's constant phase finite impulse response (FIR) filters provide fast computation, 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.

Resolution

increased by

-3 dB Bandwidth (x

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. ERes 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.

Note: While ERes improves the resolution of a trace, it cannot improve the accuracy or linearity of

the original quantization. The pass-band causes signal attenuation for signals near the cut-off

frequency. The highest frequencies passed may be slightly attenuated. Perform the filtering on

finite record lengths. Data is lost at the start and end of the waveform and the trace ends up

slightly shorter after filtering. The number of samples lost is exactly equal to the length of the

impulse response of the filter used: between 2 and 117 samples. Normally this loss (just 0.2 % of a

50,000 point trace) is not noticed. However, you might filter a record so short that no data is

output. In that case, however, the instrument would not allow you to use the ERes feature.