What is simplest way to convert digital signal 1 0 0 1 0 0 1 0 0 (i.e. 1/3 of time its ON and 2/3 of time its off) into sinusoidal signal of same frequency, which can vary from 3 KHz to 6 MHz?
If you don't care too much about being exactly sinusoidal, you could just filter the signal to make it less square.
If you don't mind a small lag in response time, and losing phase information, you could filter it very aggressively, say at a few hundred Hz, effectively turning the input PWM into a voltage. You could then apply that to a voltage-to-frequency converter circuit.
Otherwise, you'd have to build an analogue PLL, possibly using a PLL IC: http://www.sentex.ca/~mec1995/gadgets/pll/pll.html
Or if you don't mind software, interpret the signal with a microcontroller/DSP and output a matching sine (generated with a table or CORDIC) through a DAC.