This is a good introduction to using PICs for sampling repetitive waveforms...
http://circuitcellar.com/cc-blog/minimum-mass-waveform-capture/
http://circuitcellar.com/cc-blog/minimum-mass-waveform-capture/
IMO This would be impractical with a Picaxe as the sample rate (READAC > Write to Ram > Change PWM > Repeat) would be painfully slow. It would also be difficult to utilize enough RAM to acquire an adequate number of samples for meaningful data.To capture a waveform, the PWM D/A converter (PWM DAC) is set to its maximum output voltage. Then, using timing loops to generate regularly spaced sampling times (1 µs in Figure 1), the microcontroller looks at the output of the voltage comparator to determine if the incoming voltage is higher than the PWM voltage. At each sampling time, if the PWM voltage is at a higher voltage than that of the incoming waveform, the PWM value is stored in a RAM array location corresponding to that sampling time.