Does a battery powered tablet operating off my house WiFi router need a clean backup electric supply, ie a backup generator with an inverter? I can see where a desktop plugged into a wall outlet would require an inverter, but not sure about the tablet. Thanks.

Edit.  Think I asked the wrong question. Seems like the important spec is THD, just like the OLD days with stereo equipment. So, any sensitive electronic would want no more than 5% THD. I assume a tablet operating off battery power does not see or care about THD. But, the WiFi router might?THD..., clean electricity supply..., inverters... - all useful if connecting straight to the mains outlet.
anything else that converts mains power into lower volts/amps for devices such as laptops, tablets, router/modems etc already has this covered by their little black lump of plastic at the end of the cord - the power regulator.I agree with Mark on this. The power supply adapter for the tablet that converts AC of one voltage to DC  of another is pretty rugged at cleaning up power to the device thats plugged into it. 

I would suggest a power strip with SURGE suppression between generator and power supply adapter to device. Most generators are GOOD at conditioning the AC output however most dont make a clean sine wave like 60Hz AC in USA. Most make an output that resembles a rippled square wave, and this can be a problem for inductive devices like induction motors that do far better on a clean sine wave.

Battery backups ( aka UPS's ) dont like to be connected to a generator. I learned this by during a power outage I had my desktop computer powered through battery backup which was powered from my 4800 watt generator and the battery backup kept clicking to the switch over to battery at about once relay click per second as the battery backup didnt like this non sine wave output and it kept correcting for it to the desktop computer. Powering my desktop computer directly through a power strip the desktop computer was fine on the somewhat square waved 120VAC. But if the generator ran out of gas it would be like a power outage to the desktop computer, so i decided to use my laptop instead where it has a battery that it can run off of if the generator shuts off for about 1.5 hours if needed.

That said, they do make generators with a clean sine wave but they are costly! The general generators out there are pretty much pretty good and safe to use as long as your not powering induction motors off of them in which you might get lucky and the motor runs fine as well as you might find that the saw your trying to run isnt happy without a true sine wave AC source.Modern AC generators have very clean output.
This link below will help clear up any confusion.
http://yamahaef2000is.com/conventional_generator_vs_inverter_generator.html

Inverts vary in quality and power levels. Some are dirty output.
Automotive alternators can be used to generate AC. The hard part is GETTING the frequency right on 60 Hz.

The is no evidence that tablets a end smartphone perform poorly on any power adapters. The power requirements oar very low when compared to normal laptops