Center correction for the music sample

Summary
The same center correction process reported last time is performed on the music sample. Although the wavelet differentiation still introduces DC offsets to the signal, the pitch fluctuation is largely removed.

Before center correction:
http://kakyoism.webhop.net/~kakyo/0.report/47.center/audio_mitac_stereo_v2_algo23_RIAA.wav

After center correction:
http://kakyoism.webhop.net/~kakyo/0.report/47.center/audio_mitac_stereo_v2_setup28-cca1-r3484-a0.12pi.wav

Plan
Try to fully automate the process in a coarse-to-fine way, using both magnitude and phase information of the resulting audio from each Monte Carlo center shift

1. Coarse correction: Using the audio resulting from the non-corrected center info as a reference, if we sample the new center angularly with a fixed shifting radius, depending on where the Monte-Carlo test center is, some of the samples will show themselves as out-of-phase from the reference signal, while others will be in-phase; When corrected audio results from various angular positions are uniformly out-of-phase or in-phase, we know that the position of  corresponding Monte-Carlo center is far from the true center. Then by sampling in the radial dimension, we search a critical point where angular sampling gives us a mix of out-of-phase and in-phase results. The sampling resolution in this step can be very low, i.e., just a few samples will get us to the critical Monte-Carlo center.
   
2. Fine correction: We then try taking Monte-Carlo around the critical center with a higher resolution in angular and radial dimensions, and minimize the low-end spectral energy from the magnitude response of the audio results.