Line filters block rapid changes in voltage but do nothing for slower changes, which require a voltage regulator or real UPS (load is always powered by battery circuit). Try that test I mentioned where the laser printer is turned on or off, or use other loads like vacuum cleaners or power tools. Best may be an old-style fluorescent desk lamp where you have to hold a button down for 1-2 seconds until it lights up.
113VAC seems low but could be normal, if it's the no-load voltage, but you may want to test by loading down the AC outlet with something that draws at least 10 amps, like a hair dryer, vacuum cleaner, or power tool, and see how much the voltage droops. Apparently 6% droop is acceptable, and modern electronics are supposed to tolerate voltage as low as 90-100VAC, but I'd rather see only a 3% droop. Where I used to live, some of the outlets would go from 122VAC to 90VAC at 15 amps because the wire splices were loose -- all back-stabbed instead of screwed.