Sco X-1 data from paper

Wavelet Stuff

• Light Curve, Scalegrams

• Light Curve, Scalegrams

• Light Curve, Scalegrams

Points:

• Use Poisson-Corrected Wavelets to characterize noise:
  • slope -- log V(s) vs. s ~ linear ===> power law noise
  • break points ===> scale change, ...
  • QPOs

• Time dependent noise:
  • high frequency stuff (small s) is pretty invariant
  • low frequency stuff (large s) is variable (amplitude), but slope is pretty constant
  • QPO at s = 5 can come and go without affecting underlying noise (both high and low frequency)

  Above analysis took me 10 minutes with wavelets. Note each scalegram contains 2**19 = 524,288 points. Scalegrams are fast.

  Wavelets are easy to correct for counting statistics as are FFT's. I have empirically determined how the error in the correction changes with average count rate and scale, s. Maybe Jeff has done it the right way, i.e., analytically. Noise subtraction ability ==> excess noise is easy to find. Same thing is possible with FFTs, but requires throwing information away in order to get the scaled result. Throwing information away to get the same result means that extra work is being done (which is why FFTs are slower).

  Time-Frequency Routines

  We propose to investigate the virtues vs. vices of the following time-frequency techniques:
  • Short-Time Fourier Transforms
  • Gabor Transforms

  Hmmm, I guess that my overall vision is tilting toward temporal variations of signals.