Convert Sawtooth to Sinusoid with RLC Circuit

[iflabs]

A sawtooth waveform is given in the time domain with a certain period.

How does one go about converting the sawtooth to sinusoid with just resistors, capacitors, and inductors (simple RLC circuit)? We've recently covered filter circuits, so I'm betting we need to pass the signal through some filter. Any hints to get me going?

 

[vk6kro]

A sawtooth waveform contains a fundamental sinewave and all harmonics of this sine wave.

So, to recover the fundamental, you need to either pass it through a low pass filter (with a cutoff between the fundamental and its first harmonic) or pass it through a band pass filter (tuned to pass only the fundamental).

A common type of filter is the Butterworth:
http://en.wikipedia.org/wiki/Butterworth_filter
and the Chebychev filter:
http://en.wikipedia.org/wiki/Chebyshev_filter

Note that you can gradually improve the filtering by using better filters with more components, but it is very hard to eliminate all traces of the harmonics, so the waveform does not quite become a perfect sinewave.

You might like to read about sawtooth waveforms here:
http://en.wikipedia.org/wiki/Sawtooth