THe 815 is likely doing it right. I should have warned you that with wide scans the number of data points are spread out and interpolation is the result with soso accuracy. For better results use a narrower scan (span). All but the older full analog SAs have that problem. Somewhere in the manual it will give you the number of point it actually takes measurements at. Typically its some amount of memory limit or the width of the screen in Pixels.
The best approach is setup for 45mhz, maybe 50khz span and stuff that though if you have the 815T.
If you have the plain 815 (no tracking generator) set it for write hold and sweep it very slowly with signal generator or a high output noise source and you will get the passband outline. Its slow doing it that was but it works. I've used this on my 8568B as that does not have a tracking generator so I use a noise source to fill it.
FYI you can dial the VFO (5351) down to 45mhz and enough of it will be there to see in and out.
