Converting square signal into sinusiod avoiding Fourier Transform

I have a clean digitized square wave signal with a frequency around 50 kHz and I would like to convert it into a sinusoid with the same frequency and phase (don't care about amplitude). I would like to do so avoiding the stantard approach that would be  doing the Fourier tranform to measure the frequency and phase and then generating a new sinusoid. Are you aware of any other procedure?
Thank you!

What's up with the FFT-phobia? Is this some kind of homework with silly restrictions?
(Even the zero phase filter mentioned by Darin might use FFT like functions internally. )
Keeping up the facade, here's one way using "extract single tone". (Which also uses FFT internally).
Of course you could get a good initial estimate on the frequency and phase by measuring the zero crossings, then fit to a sine function with adjustable amplitude, phase and frequency using levenberg-marquardt. Suddenly, FFT seems like a better idea .
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Attachments:
SquareToSine.png ‏20 KB

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