0 - 12v square to +/- 2.5v Sine converter

[JMG]

Alright analog guru's I've got an issue. I need to take a 0 - 12v square wave of 50% duty cycle and varying frequency and produce a +/- 2.5v sine wave with 4 times the frequency of the square wave.
I'd thought about using a PIC to count the time between 2 incoming pulses, then on the third pulse, turn on the output 4 times, then count the next 2 incoming pulses and so on. I'd tough about having a 2 rails and an output, a capacitor and fet between each rail and the output, thus I can turn on a fet and the output will be pulled to one rail, the turn that fet off and turn on the other fet making the output swing through to the other rail.

Would this work? Is tis an analog design? :|

 

[FvM]

"varying frequency" isn't very specific, right?

I don't see, how your sketched circuit can generate a sine waveform. I would consider a PLL to multiply the frequency.
An almost analog solution would use a sine function generator (e.g. XR2206) or a true analog sine generator as VCO and
lock it to the input signal.