This is the result of a basic reconstruction on the LTE/MZ modulated waveform in comment #349. The reconstructed curve picked close to the actual except where it flipped polarity as indicated. The problem is where the anticipated continuation of the curve was extrapolated close to a zero crossing (highlighted in yellow) whereafter the algorithm selected the polarity-reversed curve to continue as being an arbitrarily closer fit. This might be corrected by adding a 2nd order factor to the extrapolation.

![](https://imagizer.imageshack.com/img924/1406/dbvDwa.png)

The following amplitude spectrum is a marvelous illustration of what the LTE demodulation algorithm provides. The dotted spectrum in blue is of the raw unprocessed LTE modulation test waveform. This is a jumble of indistinct peaks spread across the spectrum -- much like an actual ENSO spectrum. In red is the reconstructed spectrum corresponding to the algorithmically demodulated LTE waveform. Here one can distinctly pick out the 3 correctly positioned sine waves that were mixed together by the LTE modulation. Interesting to also note that the smaller satellite peaks are due to the incorrect extrapolation in the previous chart, and that these will disappear with a better optimized reconstruction algorithm.

![](https://imagizer.imageshack.com/img923/5825/yNI6Ml.png)

What's remarkable about this approach is the ability to reconstruct the original signal properties based on only some basic trig identities.