Have just started thinking about a signal generator. I don't want the modern type where they RC integrate on a square wave and try to filter out the harmonics, because there's a lot they don't filtered out. For noise and filtering theory I've go Goldman's book. One and only once I managed to measure a noise power spectrum (1/f noise from a photodetector). You've got to interpolate through 120 and 60 HZ. You never get rid of it out unless your whole setup if run off of batteries and you've got it all in a Faraday cage. Your voltmeter for measuring output has to be accurate square-law so reading is proportional to power. For the the bandpass you've got the problem of getting the the bandpass right for power, so you can get transfer funcetion powerwise. Power and voltage tranmsfer functions aren't the same. 3 db points work approximately for voltage, but aren't even close for power.

I had one course in noise and filtering at the U. of Wash. It got offered by the Physics Dept. But nobody at the U could teach it, so it was a night class given by a math-EE from Boeing. I have C. Shannon's orig. edit. of Information theory (1954), but that's basically all digital.