can we use supercapacitor in filter circuits?
Supercaps are not well suited to reducing ripple of something like a dumb diode rectifier power supply because they have large ESR (equivalent series resistance) compared to other types of caps.  A plain old electrolytic is better, then followed by active circuitry to flatten out the result.

In some cases, large power supply caps aren't used at all anymore.  Power supplies that do PFC (power factor correction), for example, deliberately don't have any capacitance immediately after the full wave bridge.  The raw rectified AC goes into a switching power supply directly, which adjusts its current draw to stay proportional to the input voltage.  There is still a cap after the switcher, but supercaps are even less suited for that role since the ripple frequency is much higher than the 50 or 60 Hz line frequency.  At 100 kHz or more, ESR and ripple current capability are important, and large amount of capacitance less important.