How to implement a realtime filter for an arbitrary waveform?

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I am unfamiliar with digital signal processing and would like help with the following roadblock I encountered.

I am comparing phases of two clocks using a Digital Dual Mixer Time Difference (DDMTD) implementation (Moreira, Pedro, et al. “Digital dual mixer time difference for sub-nanosecond time synchronization in Ethernet.” 2010 IEEE international frequency control symposium. Available online from the white rabbit website).

Due to some facets of the implementation, I have undesired oscillations with periods (16ns/frequency offset between clocks in ns/S).

For example:

Clock frquency difference = 10ps/s

Clock frquency difference = 50ps/s

As you could notice , lower harmonics of this noise is also present in the output.
How can I remove this unwanted noise from my output in realtime? The clock freqeuncy differences I can determine after measuring for some duration. I want this filter to activate and utilise the clock differnce data I provide to filter out noise.

Can anyone point me towards the right direction to approach this problem?

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