3 ms·
I haven't looked at his source yet, but my guess is that the power spectrum was inverted directly back to real space/"time" domain, without randomizing the phas
by ISL 13y ago
I haven't looked at his source yet, but my guess is that the power spectrum was inverted directly back to real space/"time" domain, without randomizing the phase.
Keep a grain of salt at the ready as you analyze the problem. It's a tricky thing to do "right", and even when you're done, it's not clear that "right" will be well-defined in this case.
Edit: Since the code is a *.nb form, I can't read it directly (insufficient space/desire to install the Mathematica Reader), but from what I can glean reading it as ASCII text, the sound is synthesized from in-phase cosines. Each signal at every frequency starts together, leading to a spike in amplitude. You can see each pop very clearly if you look at the wav file over a short duration in the time domain.
The relative phases of the spectra, following the analysis that Cramer's used (inverting the angular power spectrum into sound) actually are in the raw WMAP/Planck data, and may be in print. If you have the raw temperature map and are comfortable computing the angular power spectrum, you'll have access to the phase too.
I can't find a perfect reference at the moment, but to emphasize the importance of the phase in reconstructing real-space data, check out the pictures in [1].
[1] http://homepages.inf.ed.ac.uk/rbf/CVonline/LOCAL_COPIES/OWENS/LECT4/node2.html http://homepages.inf.ed.ac.uk/rbf/CVonline/LOCAL_COPIES/OWEN...