I performed in the lab some experiments regarding a spectrum analyzer and I have a few questions about its behaviour. The analyzer used was this one
At first I had to determine the spectrum of a 4kHz sinusoidal function. I obtained the expected spectrum (one stripe at 4k). I chose a sweep velocity of 0.5s/div and pass-band filter bandwidth of 100 Hz. Now I then varied the velocity, coming to the conclusion that a velocity that was less than 0.5s/div would not produce the correct spectrum, but any slower velocity would do it. At the time I didn't fully understand what the bandpass filter bandwidth meant. I just tried 100 Hz and it worked, while 300 Hz would produce a spectrum with a not so narrow stripe and 30 Hz wouldn't work. After the lab I did some research and understood that even if ideally the bandwidth of the bandpass filter is as narrow as possible, it is limited by the sweep time. Therefore, my question is: if I had increased the sweep time (less velocity), would I be able to produce correct results with a narrower bandwidth? Also, is there a mathematical expression that relates this two?
Then I did the same work but with a rectangular pulse of 400 Hz, 20% duty-cycle. I had the same bandwidth but now with a sweep of 0.2s/div. This was the minimum sweep time I could define and again, 30 Hz bandwidth still not works. My question is the same as before but with a new factor: how does the frequency of a signal relates to the sweep time. Because now I could define a sweep time smaller than my previous case, so my guess is that obviously the frequency of the signal matters. A signal with a smaller (fundamental) frequency can be swept with a bigger velocity. Again, is there any expression that relates this two?
Thanks in advance!