How do I smooth out the voltage from a pulse-charger?
The battery voltage is unlikely to change much during pulsing. See text below and measure with an oscilloscope. 

The graph below shows typical lead acid charge curves at different rates of charge and states of battery charge.  When pulse charging - when charging is off the voltage will be at about the rest state for the current state of charge and when charging is on will rise to the voltage corresponding to current state of charge and charge rate. In reality the change will be less or much less than this for short off-pulses as the battery will tend to maintain its charged state somewhat. Any resistive internal drop (V = I x R) will change immediately). 

If you were pulse charging at say C/5 you'd get perhaps under 1V rise when when the battery was fully discharged and perhaps 3+ Volt rise when the battery was fully charged. 



A filter that accomodates that is easily built. To get low drop you'll want an inductive input filter. Placing a capacitor at the input to the filter that is large enough to noticeably damp the pulse will also remove any benefit that the pulse charger may have. I'll not go into much detail here - ask if interested. An LC filter designed to supply the energy during the 20 mS pulses is needed. If current is in the amps range you will probably end up with an inductor wound on a standard transformer core, and a transformer winding of around 12V rating and rated at at least the maximum current you will draw is required. Capacitor TBD but as a guide a 10,000 uF supplying all the energy by itself (no battery) would drop 1 Volt when 1 amp was drawn during a 20 mS break. In combination with an inductor and the battery it will do much better.  

Ideally, if you MUST pulse charge the battery, do so when it is not connected to and/or powering the equipment. 

Whether pulse charging is beneficial is much debated. It does appear to have some benefit but not necessarily for any of the reasons most  usually thought. If your battery is in good condition and kept charged by a competent charger then pulse charging is unlikely to be very beneficial.