Sinusoidal Signal & Narrow RBW

What happens when a sinusoidal signal is encountered? We know that as a
mixing product is swept past the IF filter, an analyzer traces out the shape of
the filter on the display. If the filter shape is spread over many display points,
then we encounter a situation in which the displayed signal only rises as the
mixing product approaches the center frequency of the filter and only falls as
the mixing product moves away from the filter center frequency. In either of
these cases, the pos-peak and neg-peak detectors sense an amplitude change
in only one direction, and, according to the normal detection algorithm, the
maximum value in each bucket is displayed. See Figure 2-24.

What happens when the resolution bandwidth is narrow, relative to a bucket?
The signal will both rise and fall during the bucket. If the bucket happens
to be an odd-numbered one, all is well. The maximum value encountered in
the bucket is simply plotted as the next data point. However, if the bucket is
even-numbered, then the minimum value in the bucket is plotted. Depending
on the ratio of resolution bandwidth to bucket width, the minimum value can
differ from the true peak value (the one we want displayed) by a little or a lot.
In the extreme, when the bucket is much wider than the resolution bandwidth,
the difference between the maximum and minimum values encountered in
the bucket is the full difference between the peak signal value and the noise.
This is true for the example in Figure 2-25. See bucket 6. The peak value of
the previous bucket is always compared to that of the current bucket. The
greater of the two values is displayed if the bucket number is odd as depicted
in bucket 7. The signal peak actually occurs in bucket 6 but is not displayed
until bucket 7.

Figure 2-24. Normal detection displays maximum values in buckets
where signal only rises or only falls