matched filter for doppler
you sample the interval and build a filter for each frequency shift, unless you don’t need to, like in typical carrier/phase recovery schemes. 

You make a bank of filters, particularly if Doppler is of itself, of interest.  In SONAR, tones have better Doppler resolution, and the DFT provide a bank of filters.

The ambiguity function function for the waveform will show how much loss you can tradeoff for the frequency sampling you choose.  

Each waveform will have different loss for frequency miss-match.  The ambiguity function also accounts for delay resolution.   

A waveform like hyperbolic FM is robust to Doppler so a single waveform covers a wide range of possible shifts.

Both miss-matches can couple. 

In comms, Doppler compensation is usually a matter of compensation of the frequency shift, not full time dilation.  Shifting a matched filter is a matter of frequency shifting and can be accommodated in carrier/ phase recovery.