Digital Resolution Filters

On the other hand, the rise time of a filter is inversely proportional to its
bandwidth, and if we include a constant of proportionality, k, then:

The value of k is in the 2 to 3 range for the synchronously-tuned,
near-Gaussian filters used in many Agilent analyzers.

The important message here is that a change in resolution has a dramatic
effect on sweep time. Most Agilent analyzers provide values in a 1, 3, 10
sequence or in ratios roughly equaling the square root of 10. So sweep time
is affected by a factor of about 10 with each step in resolution. Agilent PSA
Series spectrum analyzers offer bandwidth steps of just 10% for an even
better compromise among span, resolution, and sweep time.

Spectrum analyzers automatically couple sweep time to the span and
resolution bandwidth settings. Sweep time is adjusted to maintain a calibrated
display. If a sweep time longer than the maximum available is called for,
the analyzer indicates that the display is uncalibrated with a 'Meas Uncal'
message in the upper-right part of the graticule. We are allowed to override
the automatic setting and set sweep time manually if the need arises.

Digital resolution filters
The digital resolution filters used in Agilent spectrum analyzers have an
effect on sweep time that is different from the effects we've just discussed for
analog filters. For swept analysis, the speed of digitally implemented filters
can show a 2 to 4 times improvement. FFT-based digital filters show an even
greater difference. This difference occurs because the signal being analyzed
is processed in frequency blocks, depending upon the particular analyzer.
For example, if the frequency block was 1 kHz, then when we select a 10 Hz
resolution bandwidth, the analyzer is in effect simultaneously processing the
data in each 1 kHz block through 100 contiguous 10 Hz filters. If the digital
processing were instantaneous, we would expect sweep time to be reduced
by a factor of 100. In practice, the reduction factor is less, but is still
significant. For more information on the advantages of digital processing,
refer to Chapter 3