Try using a different amp. Some amps have all these extra controls like "hum", ripple, as mentioned already. These can really get amplified if you have a weird signal chain.
In my case I started running a compressor between the amp and the cab, which really improved the feel. But it introduced constant low-frequency hum, which I noticed one day. Well, in my snapshot for the dirty sound, I just dialed down that "hum" parameter to 0, and the issue was fixed. Some amps do weird stuff.
Crackle and pop could be from static electricity. I've noticed the original Helix even having its capacitance triggered from static electricity, when it was on a rug. All sorts of menus would pop up constantly.